We provide sets practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on sets skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

#### List of sets Questions

Question No | Questions | Class |
---|---|---|

1 | Let ( boldsymbol{O}= ) Set of odd natural numbers ( = ) ( {1,3,5,7,9, dots} ) and ( E=operatorname{set} ) of even natural numbers ( ={2,4,6,8,10, dots dots .} ) Then show that ( 3 in E ) | 11 |

2 | Draw Venn diagrams to illustrate ( boldsymbol{A} cup ) ( (boldsymbol{B} cap boldsymbol{C}) ) | 11 |

3 | The set of fractions between the natural numbers 3 and 4 is a : A. Finite set B. Null set c. Infinite set D. singleton set | 11 |

4 | Suppose ( A_{1}, A_{2}, dots, A_{30} ) are thirty sets each having 5 elements and ( B_{1}, B_{2}, dots, B_{n} ) are n sets each with 3 elements. Let ( bigcup_{i=1}^{30} A_{i}=bigcup_{j=1}^{n} B_{j}=S ) and each elements of ( S ) belongs to exactly 10 of the ( A_{i} ) and exactly 9 of the ( B_{j} . ) Then ( n ) is equal to- A . 35 B. 45 5 ( c .55 ) D. 65 | 11 |

5 | Find total number of subsets of ( mathrm{B}={mathrm{a} ) ( mathbf{b}, mathbf{c}} ) | 11 |

6 | Given ( boldsymbol{A}=mathbf{2}, mathbf{3}, boldsymbol{B}=mathbf{4}, mathbf{5}, boldsymbol{C}=mathbf{5}, mathbf{6}, ) find (i) ( boldsymbol{A} times(boldsymbol{B} cap boldsymbol{C})=ldots ldots ) (ii) ( (boldsymbol{A} times boldsymbol{B}) cup(boldsymbol{B} times boldsymbol{C})=ldots ldots ) | 11 |

7 | ( mathrm{U}={1,2,3,4,5,6,7,8,9,10} ) ( mathrm{A}={2,4,6,8,10}, B={1,3,5,7,8,10} ) Find ( (A cup B) ) | 11 |

8 | If ( boldsymbol{A}={mathbf{1}, mathbf{2}, mathbf{3}}, boldsymbol{B}={mathbf{3}, boldsymbol{4}} ) and ( boldsymbol{C}= ) ( {1,3,5}, ) then ( A times(B-C)= ) A ( cdot(A times B)-(A times C) ) в. ( (A times B)+(A times C) ) c. ( (A times B)-(B times C) ) D. ( (A times B)-(C times A) ) | 11 |

9 | Identify the type of set ( boldsymbol{B}={boldsymbol{x}: boldsymbol{x} boldsymbol{epsilon} boldsymbol{W}, boldsymbol{x}=boldsymbol{2} boldsymbol{n}} ) A. Finite Set B. Null Set c. Infinite Set D. singleton set | 11 |

10 | For any two sets ( A ) and ( B ), show that the following statements are equivalent. (i) ( boldsymbol{A} subset boldsymbol{B} ) (ii) ( boldsymbol{A}-boldsymbol{B}=boldsymbol{phi} ) (iii) ( boldsymbol{A} cup boldsymbol{B}=boldsymbol{B} ) (iv) ( boldsymbol{A} cap boldsymbol{B}=boldsymbol{A} ) | 11 |

11 | Write down all possible subsets of the following set. {1,{1}} | 11 |

12 | ( a epsilon{a, b, c}, ) then ( {a} ) is a subset of ( {a, b, c} .(text { Enter } 1 text { if true or } 0 text { otherwise }) ) | 11 |

13 | Which one of the following is not true? ( mathbf{A} cdot A backslash B=A cap B^{prime} ) в. ( A backslash B=A cap B ) C ( . A backslash B=(A cup B) cap B^{prime} ) D. ( A backslash B=(A cup B) backslash B ) | 11 |

14 | If ( A={1,2,3,4,5,6,7,8} ) and ( B={1,3,5 ) 73, then find ( A-B ) and ( A cap B ) ( A cdot{3,5} ) and {2,4,6} B. {2,4,6) and (1,5} c. {2,4,6,7} and (1,3,5,6) D. {2,4,6,8} and {1,3,5,7} | 11 |

15 | Draw a Venn diagram, showing sub-set relations of the following sets. ( boldsymbol{A}={mathbf{2}, boldsymbol{4}} quad boldsymbol{B}=left{boldsymbol{x} mid boldsymbol{x}=boldsymbol{2}^{n}, boldsymbol{n} leqright. ) ( mathbf{5}, boldsymbol{n} in boldsymbol{N}} ) ( C={x mid x text { is an even natural number } leq ) ( mathbf{1 6}} ) | 11 |

16 | Place the elements of the following sets in the proper location on the given Venn diagram. ( boldsymbol{U}={mathbf{5}, mathbf{6}, mathbf{7}, mathbf{8}, mathbf{9}, mathbf{1 0}, mathbf{1 1}, mathbf{1 2}, mathbf{1 3}} ) ( M={5,8,10,11}, N={5,6,7,9,10} ) | 11 |

17 | Let ( boldsymbol{A}={1,2,3,4,5,6,7,8,9,10} . ) Then the number of subsets of ( A ) containing exactly two elements is A . 20 B. 40 c. 45 D. 90 | 11 |

18 | Number of ( P_{2} ) and ( P_{3} ) viewers. | 11 |

19 | If ( A={a, b, c, d, e}, B={a, c, e, g} ) and ( C= ) ( {b, d, e, g} ) then which of the following is true? A ( cdot C subset(A cup B) ) B . ( C subset(A cap B) ) c. ( A cup B=A cup C ) D. Both(1) and (3) | 11 |

20 | Let ( boldsymbol{A}={mathbf{3}, mathbf{6}, mathbf{1 2}, mathbf{1 5}, mathbf{1 8}, mathbf{2 1}}, boldsymbol{B}= ) ( {mathbf{4}, mathbf{8}, mathbf{1 2}, mathbf{1 6}, mathbf{2 0}}, boldsymbol{C}= ) ( {mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}, mathbf{1 2}, mathbf{1 4}, mathbf{1 6}} ) and ( boldsymbol{D}= ) ( {mathbf{5}, mathbf{1 0}, mathbf{1 5}, mathbf{2 0}} . ) Find ( boldsymbol{B}-boldsymbol{D} ) | 11 |

21 | Given, ( boldsymbol{A}={text { Triangles }}, boldsymbol{B}={ ) Isosceles triangles ( } ) ( C={text { Equilateral triangles }} . ) State whether the following statement are correct or incorrect. Give reasons. ( boldsymbol{C} subset boldsymbol{A} ) | 11 |

22 | If ( boldsymbol{A}=(boldsymbol{6}, boldsymbol{7}, boldsymbol{8}, boldsymbol{9}), boldsymbol{B}=(boldsymbol{4}, boldsymbol{6}, boldsymbol{8}, boldsymbol{1} boldsymbol{0}) ) and ( boldsymbol{C}={boldsymbol{x}: boldsymbol{x} boldsymbol{epsilon} boldsymbol{N}: boldsymbol{2}<boldsymbol{x} leq mathbf{7}} ; ) find : ( boldsymbol{n}(boldsymbol{B}-(boldsymbol{A}-boldsymbol{C})) ) | 11 |

23 | If ( boldsymbol{P}={text { factors of } 36} ) and ( boldsymbol{Q}={ ) factors of ( 48}, ) find ( Q-P ) | 11 |

24 | Use the given figure to find: Given, ( n(xi)=52, n(A)=43 ) and ( boldsymbol{n}(boldsymbol{B})=mathbf{2 7} ) ( boldsymbol{n}(boldsymbol{A}-boldsymbol{B}) ) | 11 |

25 | Find the intersection of ( A ) and ( B, ) by representing using Venn diagram: ( boldsymbol{A}={mathbf{1}, mathbf{3}, mathbf{5}, mathbf{7}}, boldsymbol{B}={mathbf{2}, mathbf{5}, mathbf{7}, mathbf{1 0}, mathbf{1 2}} ) ( mathbf{A} cdot{1,3,5,7} ) B ( cdot{5,7} ) ( mathbf{c} cdot{1,2,3,5,7,10} ) D. None of these | 11 |

26 | State whether given set is empty or not? Set of even prime numbers | 11 |

27 | Write down all possible subsets of the following set. ( {a, b, c} ) | 11 |

28 | Which set is the subset of the set containing all the whole numbers? ( mathbf{A} cdot{1,2,3,4, dots dots .} ) в. {1} ( c cdot{0} ) D. All of the above | 11 |

29 | Given ( xi={x: x text { is a natural number }} ) ( A={x: x text { is an even number } x in N} ) ( mathrm{B}={mathrm{x}: mathrm{x} text { is an odd number, } mathrm{x} in mathrm{N}} ) Then ( (boldsymbol{B} cap boldsymbol{A})-(boldsymbol{x}-boldsymbol{A})=dots ) ( A cdot phi ) в. ( c . B ) D. ( A-B ) | 11 |

30 | The ( operatorname{set} A=x:|2 x+3|<7 ) is equal to A. ( -10<2 x<4 ) в. ( -11<2 x<4 ) c. ( -12<2 x<4 ) D. ( -13<2 x<4 ) | 11 |

31 | If ( S= ) ( left{x in N: 2+log _{2} sqrt{x+1}>1-log _{1 / 2}right. ) then ( mathbf{A} cdot S=1 ) B. ( S=Z ) c. ( S=N ) D. none of these | 11 |

32 | Use the given Venn-diagram to find the number of elements in ( A cup B ) | 11 |

33 | Let ( boldsymbol{U} ) be the universal set and ( boldsymbol{A} cup boldsymbol{B} cup ) ( C=U . ) Then ( {(boldsymbol{A}-boldsymbol{B}) cup(boldsymbol{B}-boldsymbol{C}) cup(boldsymbol{C}-boldsymbol{A})}^{prime} ) is equal to A. ( A cup B cup C ) в. ( A cup(B cap C) ) c. ( A cap B cap C ) D. ( A cap(B cup C) ) | 11 |

34 | Of 28 people in a park, 12 are children and the rest are adults. 8 people have to leave at ( 3 mathrm{pm} ; ) the rest do not. If, after 3 ( mathrm{pm}, ) there are 6 children still in the park, how many adults are still in the park? A . 14 B . 18 c. 15 D. 16 | 11 |

35 | 000 0 0 ( infty ) 00 | 11 |

36 | A survey conducted on 600 students of B. A part I classes of a collage gave the following report. Out of 600 students, 307 took economics, 198 took history, 230 took sociology, 65 took history and economics, 45 took economics and sociology, 31 took sociology and history and 10 took all the three subjects. The report sounded very impressive, but the surveyor was fired. Why? | 11 |

37 | Is the following pair of sets equal? Give reasons. ( A={2,3}, B={x: x ) is a solution of ( left.boldsymbol{x}^{2}+mathbf{5} boldsymbol{x}+boldsymbol{6}=mathbf{0}right} ) A. True B. False | 11 |

38 | In an organization of pollution control board, engineers are represented by a circle, legal experts by a square and environmentalist by a triangle. Who is most represented in the board as shown in the figure? A. Environmentalists B. Engineers with legal background c. Legal Experts D. Environmentalists with Engineering background | 11 |

39 | If ( A Delta B=A cup B, ) then which of the following can be correct? A ( . A=B ) в. ( A cap B=phi ) ( mathbf{c} cdot A Delta B=phi ) D. ( A Delta B=A sim B ) | 11 |

40 | If ( boldsymbol{A}=(mathbf{6}, mathbf{7}, mathbf{8}, mathbf{9}), boldsymbol{B}=(mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}) ) and ( C={x: x in N: 2<x leq 7} ; ) find : ( B-C ) A ( cdot{4,6} ) в. {4,6,8} c. {6,8,10} D. {8,10} | 11 |

41 | Given, ( xi={ ) Natural numbers between ( 25 text { and } 45} ; A={text { even numbers }} ) and ( B ) ( {text { multiples of } 3} ) then ( n(A)+n(B)= ) ( boldsymbol{n}(boldsymbol{A} cup boldsymbol{B})+boldsymbol{n}(boldsymbol{A} cap boldsymbol{B}) . ) If true enter 1 else 0 | 11 |

42 | State which of the following are finite sets. ( (i){x: x in N} ) and ( (x-1)(x-2)=0 ) ( (i i){x: x in N} ) and ( x ) is prime. ( (i i){x: x in N} ) and ( x ) is odd A . (i) only B. ( (i),(i i) ) and ( (i i i) ) c. ( (i) ) and ( (i i) ) D. (ii) and (iii) | 11 |

43 | Let ( boldsymbol{A}={1,2,3,4} ) and ( B={2,4,5,6} ) Find ( boldsymbol{A} cap boldsymbol{B} ) | 11 |

44 | In a college of 300 students, every student reads 5 newspapers and every newspaper is read by 60 students. The number of newspapers is A. at least 30 B. at most 20 c. exactly 25 D. none of these | 11 |

45 | In the Venn diagram, ( boldsymbol{xi} ) F UG cup ( boldsymbol{H} ). The shaded region represents: ( mathbf{A} cdot G^{prime} cap F ) ( mathbf{B} cdot(F cap H) cup G^{prime} ) ( mathbf{c} cdot(F cap H) cap G^{prime} ) ( mathbf{D} cdot(F cap G)^{prime} cap H ) | 11 |

46 | If ( A=(6,7,8,9), B=(4,6,8,10) ) and ( C={x ) ( boldsymbol{x} boldsymbol{epsilon} boldsymbol{N}: boldsymbol{2}<boldsymbol{x} leq mathbf{7}} ; ) find : ( A-B ) A ( cdot{6,8} ) в. {7,9} c. {6,9} D. {6,7,9,10} | 11 |

47 | Verify whether ( boldsymbol{A} subset boldsymbol{B} ) for the sets ( boldsymbol{A}= ) ( {{a, b, c}}, B={1,{a, b, c}, 2} ) | 11 |

48 | (1979) If X and Y are two sets, then X n(XUY) equals. (a) x (b) Y (d) None of these. | 11 |

49 | Identify the type of set ( boldsymbol{A}={boldsymbol{x} mid boldsymbol{x} epsilon boldsymbol{R}, boldsymbol{2} leq boldsymbol{x} leq boldsymbol{3}} ) A. Finite Set B. Infinite Set c. Null set D. singleton set | 11 |

50 | Which of the following has only one subset? A ( cdot{0,1} ) B . {1} ( c cdot{0} ) ( D cdot{} ) | 11 |

51 | Let ( boldsymbol{A}={1,2,3,4,5,6} ) and ( B= ) ( {6,7,8} . ) Find ( A triangle B ) and draw Venn diagram | 11 |

52 | Let ( n ) be a positive integer. Call a non- empty subset ( S ) of ( {1,2, ldots, n} ) good, if the arithmetic mean of the elements of ( S, ) is also an integer. Further let ( t_{n} ) denote the number of good subsets of ( {1,2, ldots, n} . ) Prove that ( t_{n} ) and ( n ) are both odd or both even | 11 |

53 | Statements: (i) All rats are cats. (ii) All cats are dogs. Conclusions: (i) All rats are dogs. (ii) Some cats are rats. A. Only conclusion I is true B. Only conclusion Il is true c. Both conclusion I and II are true D. Neither conclusionl nor conclusion II is true | 11 |

54 | The diagram given below represents those students who play Cricket, Football and Kabaddi. Study the diagram and identify the students who play all the three games. ( mathbf{A} cdot P+Q+R ) в. ( S ) ( mathbf{c} cdot S+T+V ) D. ( V+T ) | 11 |

55 | If ( mathbf{A}, mathbf{B} ) and ( mathbf{C} ) are three sets such that ( mathbf{A} cap mathbf{B}=mathbf{A} cap mathbf{C} ) and ( mathbf{A} cup mathbf{B}=mathbf{A} cup mathbf{C} ) then A ( . A=B ) B. ( A=C ) c. ( mathrm{B}=mathrm{C} ) ( mathbf{D} cdot A cap mathbf{B}=phi ) | 11 |

56 | Find the intersection of ( boldsymbol{A} ) and ( boldsymbol{B}, ) and represent it by Venn diagram: ( boldsymbol{A}={mathbf{1}, mathbf{2}, mathbf{3}}, boldsymbol{B}={mathbf{5}, boldsymbol{4}, mathbf{7}} ) | 11 |

57 | Let ( S={2,4,6,8, dots . .20} . ) What is the maximum number of subsets does ( boldsymbol{S} ) have ? A . 10 B . 20 c. 512 D. 1024 | 11 |

58 | In a town of 10,000 families it was found that ( 40 % ) families buy newspaper ( A, 20 % ) buy newspaper ( B ) and ( 10 % ) buy newspaper ( C, 5 % ) families buy ( A ) and ( B ) ( 3 % ) buy ( B ) and ( C ) and ( 4 % ) buy ( A ) and ( C . ) If ( 2 % ) families buy all three newspapers, find number of families which buy None of ( boldsymbol{A}, boldsymbol{B}, boldsymbol{C} ) | 11 |

59 | In a survey it was found that 21 persons liked product ( P_{1}, 26 ) liked product ( P_{2} ) and 29 liked product ( P_{3} ). If 14 persons liked products ( P_{1} ) and ( P_{2} ; 12 ) persons liked product ( P_{3} ) and ( P_{1} ; 14 ) persons liked products ( P_{2} ) and ( P_{3} ) and 8 liked all the three products. Find how many liked product ( P_{3} ) only. | 11 |

60 | Draw the venn diagram to illustrate ( (boldsymbol{A} cup boldsymbol{B}) ) | 11 |

61 | Identify the type of ( operatorname{set} A^{prime}={1,2,6,7} ) and ( boldsymbol{B}={mathbf{6}, mathbf{1}, mathbf{2}, mathbf{7}, mathbf{7}} ) A. Overlapping Sets B. Unequal Sets c. Equal sets D. None of these | 11 |

62 | ( lim _{x rightarrow 0} frac{1-cos (1-cos 2 x)}{x^{4}} ) | 11 |

63 | 16. Out of 1865 people, 660 can speak English and 1305 can speak Marathi. But, 120 per- sons can’t speak either lan- guage. Then how many can speak both languages? (1) 220 (2) 440 (3) 120 (4) 1085 | 11 |

64 | The Venn diagram shows the sets ( boldsymbol{xi}, boldsymbol{P}, boldsymbol{Q} ) and ( boldsymbol{R} ). Which of the following is not true? ( mathbf{A} cdot P cap Q neq phi ) в. ( R subset Q ) ( mathbf{c} cdot(P cap R) subset Q ) D. ( (P cap Q)=R ) | 11 |

65 | The following table shows the percentage of the students of a school who participated in Election and Drawing competitions. Competition Election Drawing | 11 |

66 | In the given figure, what percent of the circle is occupied by sector ( C ). ( 33 frac{1}{3} % ) ( 22 frac{2}{9} % ) ( 16 frac{2}{3} % ) | 11 |

67 | All the students of a batch opted Psychology, Business, or both. ( 73 % ) of the students opted Psychology and ( 62 % ) opted Business. If there are 220 students, how many of them opted for both Psychology and business? ( mathbf{A} cdot 60 ) в. 100 c. 77 D. 35 | 11 |

68 | If ( A ) and ( B ) are two disjoint sets and ( N ) is the universal set then ( boldsymbol{A}^{c} cup ) ( left[(boldsymbol{A} cup boldsymbol{B}) cap boldsymbol{B}^{c}right] ) is ( A cdot phi ) B. A ( c . ) в D. | 11 |

69 | Let ( boldsymbol{A}={mathbf{3}, mathbf{6}, mathbf{1 2}, mathbf{1 5}, mathbf{1 8}, mathbf{2 1}}, boldsymbol{B}= ) ( {mathbf{4}, mathbf{8}, mathbf{1 2}, mathbf{1 6}, mathbf{2 0}}, boldsymbol{C}= ) ( {mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}, mathbf{1 2}, mathbf{1 4}, mathbf{1 6}} ) and ( boldsymbol{D}= ) ( {mathbf{5}, mathbf{1 0}, mathbf{1 5}, mathbf{2 0}} . ) Find ( boldsymbol{B}-boldsymbol{A} ) | 11 |

70 | If ( boldsymbol{A}-boldsymbol{B}=boldsymbol{phi}, ) then relation between ( mathbf{A} ) and B is This question has multiple correct options ( mathbf{A} cdot A neq B ) в. ( B subset A ) c. ( A subset B ) D. ( A=B ) | 11 |

71 | State True or False. The set represented by the shaded portion of the following Venn- diagram is: ( (B-A)^{prime} ) A. True B. False | 11 |

72 | n the given diagram, the boys who are athletic and disciplined are indicated by which number? ( A ) 3. 2 ( c_{1} ) ( D ) | 11 |

73 | If ( boldsymbol{A}={boldsymbol{p}, boldsymbol{q}, boldsymbol{r}, boldsymbol{s}}, boldsymbol{B}={boldsymbol{r}, boldsymbol{s}, boldsymbol{t}, boldsymbol{u}}, ) then ( boldsymbol{A} / boldsymbol{B} ) is: ( A cdot(p, q) ) ( B cdot{r, s} ) c. ( {t, u} ) D. ( {p, q, t, u} ) | 11 |

74 | In a party, 70 guests were to be served tea or coffee after dinner. There were 52 guests who preferred tea while 37 preferred coffee. Each of the guests liked one or the other beverage. How many guests liked both tea and coffee? A . 15 B . 18 c. 19 D. 33 | 11 |

75 | ( {a, b} ) is a subset of ( {b, c, a} ).If true enter 1 else 0 | 11 |

76 | Let ( boldsymbol{A}={1, mathbf{3}, mathbf{5}, mathbf{7}, dots .} ) and ( boldsymbol{B}= ) {1,2,3,4,5} Then ( A ) and ( B ) are A. Finite and infinite set respectively B. Infinite and finite set respectively c. Both Infinite sets D. Both finite sets | 11 |

77 | From the given venn diagram, is ( boldsymbol{A} cap boldsymbol{B}^{prime} ) and ( A-B ) are equal. ( (text { Enter } 1 ) if true or otherwise | 11 |

78 | Which of the following sets of real numbers is such that if ( x ) and ( y ) are the elements of the set, then the sum of ( x ) and y is also an element of the set: I. The set of negative integers II. The set of rational numbers III. The set of irrational numbers A. None B . I only c. I and II only D. Il and III only E . I, II, and III | 11 |

79 | Let ( A={10,15,20,25,30,35,40,45} 50 ) ( B={1,5,10,15,20,30} ) and ( C={1,5,15 ) ( 20,35,45,3 . ) Verify ( A backslash(B cap C)=(A backslash ) ( boldsymbol{B}) cup(boldsymbol{A} backslash boldsymbol{C}) ) | 11 |

80 | What is the percentage of persons who read only two papers? A ( .19 % ) (年 ( 1.1 % ) B. ( 31 % ) c. ( 44 % ) D. None of the above | 11 |

81 | State the following pair of sets are equal or not If they are equal then write 1 , else 0 ( mathrm{E}=left{x: x^{2}+8 x-9=0right} ) and ( mathrm{F}={1,-9} ) | 11 |

82 | For any two sets of ( A ) and ( B ), prove that ( boldsymbol{B}^{prime} subset boldsymbol{A}^{prime} Rightarrow boldsymbol{A} subset boldsymbol{B} ) | 11 |

83 | ( f(x)={x: x leq 10, x in N}, A={x: x geq 4} ) and ( mathrm{B}={x: 2<x<7} ; ) find the number of equal sets. | 11 |

84 | Let ( P ) and ( Q ) be two sets then what is ( left(boldsymbol{P} cap boldsymbol{Q}^{prime}right) cup(boldsymbol{P} cup boldsymbol{Q})^{prime} ) equal to ( ? ) A ( cdotleft(P cap Q^{prime}right) cup(P cup Q)^{prime}=xi cap Q^{prime}=xi cap Q^{prime}=xi ) B . ( left(P cup Q^{prime}right) cup(P cup Q)^{prime}=xi cap Q^{prime}=xi cap Q^{prime}=xi ) C ( cdotleft(P cap Q^{prime}right) cup(P cap Q)^{prime}=xi cap Q^{prime}=xi cap Q^{prime}=xi ) D. none of the above | 11 |

85 | In a class, 20 opted for Physics, 17 for Maths, 5 for both and 10 for other subjects. The class contains how many students? A . 35 B. 42 ( c .52 ) D. 60 | 11 |

86 | Say true or false: ( A={x: x in N text { and } 5<x leq 6} ) is an empty set. A. True B. False | 11 |

87 | If ( boldsymbol{A} cap boldsymbol{B}^{prime}=boldsymbol{phi}, ) then show that ( boldsymbol{A}=boldsymbol{A} cap ) ( B ) and hence show that ( A sqsubseteq B ) | 11 |

88 | luz 15 do TCE B = An ana 45. If A, B and C are three sets such that A AUB= AUC, then (a) A=C (b) B=C c) AB= (d) A=B [2009) | 11 |

89 | Given that ( boldsymbol{U}= ) ( {3,7,9,11,15,17,18}, M= ) {3,7,9,11} and ( N={7,11,15,17} ) Find (i) ( boldsymbol{M}-boldsymbol{N} ) (ii) ( boldsymbol{N}-boldsymbol{M} ) (iii) ( N^{prime}-M ) (iv) ( M^{prime}-N ) ( (v) M cap(M-N) ) ( (v i) N cup(N-M) ) (vii) ( boldsymbol{n}(boldsymbol{M}-boldsymbol{N}) ) | 11 |

90 | set of rational numbers is ( left{-mathbf{6},-mathbf{5} frac{mathbf{3}}{mathbf{4}},-sqrt{mathbf{4}},-frac{mathbf{3}}{mathbf{5}},-frac{mathbf{3}}{mathbf{8}}, mathbf{0}, frac{mathbf{4}}{mathbf{5}}, mathbf{1}, mathbf{1} frac{mathbf{2}}{mathbf{3}}, mathbf{3}right. ) A. True B. False | 11 |

91 | f ( n(A)=7, n(B)=8 ) then find the maximum and minimum number of elements of ( A U B ) | 11 |

92 | Represent set ( A, B, C ) such that ( A subset ) ( boldsymbol{B}, boldsymbol{A} cap boldsymbol{C}=boldsymbol{phi} ) and ( boldsymbol{B} cap boldsymbol{C} neq boldsymbol{phi} ) by Venn diagram. The number of separate regions representing ( boldsymbol{A} cup(boldsymbol{B} cap boldsymbol{C}) ) is/are: | 11 |

93 | Let ( A={0,1,2,3,4}, B={1,-2,3,4,5,6} ) and ( C={2,4,6,7} ) (i) Show that ( boldsymbol{A} cup(boldsymbol{B} cap boldsymbol{C})=(boldsymbol{A} cup ) ( boldsymbol{B}) cap(boldsymbol{A} cup boldsymbol{C}) ) (ii) Verify this relation using Venn diagram. | 11 |

94 | Let ( boldsymbol{A}={mathbf{1}, mathbf{2}, mathbf{3}, mathbf{4}} ) ( boldsymbol{S}={(boldsymbol{a}, boldsymbol{b}) ; boldsymbol{a}, boldsymbol{b} in boldsymbol{A}, boldsymbol{a} text { divides } boldsymbol{b}}, ) write down ( S ) explicitly | 11 |

95 | Which of the following Venn diagrams correctly represents Jaipur, Rajasthan, and India? ( A ) B. ( c ) D. | 11 |

96 | Find union of ( A ) and ( B, ) and represent it using Venn diagram: ( boldsymbol{A}={1,2,3,4,5}, B={4,5,7,9} ) | 11 |

97 | Classify ( D=left{x mid x=2^{n}, n in Nright} ) as ‘finite’ or ‘infinite’. A . Infinite B. Finite c. Data insufficient D. None of these | 11 |

98 | In a city, three daily newspapers ( A, B, C ) are published, ( 42 % ) read ( A ; 51 % ) read ( B ); ( 68 % ) read ( C ; 30 % ) read ( A ) and ( B ; 28 % ) read ( mathrm{B} ) and ( mathrm{C} ; 36 % ) read ( mathrm{A} ) and ( mathrm{C} ; 8 % ) do not read any of the three newspapers. What is the percentage of persons who read only one paper? ( A .38 % ) в. ( 48 % ) ( c .51 % ) D. None of the above | 11 |

99 | Verify: ( boldsymbol{A}^{prime} cap boldsymbol{B}=boldsymbol{B}-(boldsymbol{A} cap boldsymbol{B}) ) A. True B. False | 11 |

100 | The shaded part of the figure is ( mathbf{A} cdot A cap B ) В. ( A cup B ) ( c cdot A+B ) ( mathbf{D} cdot cup-A ) | 11 |

101 | Draw a Venn-diagram to show the relationship between two overlapping sets ( A ) and ( B ). Now shade the region representing ( boldsymbol{A} cap boldsymbol{B} ) | 11 |

102 | In a group of 50 persons, 14 drink tea but not coffee and 30 drink tea. Find how many drink coffee but not tea? | 11 |

103 | Compute ( boldsymbol{P}(boldsymbol{A} mid boldsymbol{B}) ) if ( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 5} ) and ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=mathbf{0 . 3 2} ) | 11 |

104 | 35. Two sets A and B are as under : A = {(a, b) € RXR :/ a -5/<1 and| b – 51<1}; B= {(a,b) € RXR:40a-6)2 +9(6-5)= 36}. Then : [JEE M 2018] (a) ACB (b) AnB=0 (an empty set) (c) neither ACB nor BCA (d) BCA | 11 |

105 | The elements of ( boldsymbol{A} cap boldsymbol{B}^{prime} ) are: | 11 |

106 | Shade the region that represents the set ( boldsymbol{P} cap boldsymbol{Q}^{prime} ) in figure | 11 |

107 | ( boldsymbol{U}={boldsymbol{a}, boldsymbol{b}, boldsymbol{c}, boldsymbol{d}, boldsymbol{e}, boldsymbol{f}, boldsymbol{g}},left(boldsymbol{A}^{prime}right)={boldsymbol{b}, boldsymbol{d}, boldsymbol{f}} ) show that Venn diagram. | 11 |

108 | From the given diagram, find the elements of: ( A-(B cap C) ) and ( (A-B) cup(A-C) ) and enter 1 or 0 respectively if the given relation holds True or False: ( A-(B cap C)=(A-B) cup ) ( (A-C) ) | 11 |

109 | If ( A={1,2,3,4}, ) then the number of subsets of ( A ) that contain the element 2 but not ( 3, ) is A . 16 B. 4 c. 8 D. 24 | 11 |

110 | Given ( A={x: x in N text { and } 3<x leq 6} ) and ( mathrm{B}={x: x in W text { and } x<4}, ) then find ( : B-A ) | 11 |

111 | f ( boldsymbol{A}={mathbf{2}, mathbf{3}, mathbf{4}, mathbf{5}, mathbf{6}, mathbf{7}} ) and ( boldsymbol{B}= ) ( {3,5,7,9,11,13}, ) then find ( A-B ) and ( boldsymbol{B}-boldsymbol{A} ) | 11 |

112 | The number of subsets of the ( operatorname{set} A= ) ( left{a_{1}, a_{2}, dots dots dots a_{n}right} ) which contain even number of elements is A ( cdot 2^{n-1} ) B . ( 2^{n}-1 ) c. ( 2^{n}-2 ) D ( cdot 2^{n} ) | 11 |

113 | ( 10 % ) of all aliens are capable of intelligent thought and have more than 3 arms, and ( 75 % ) of aliens with 3 arms or less are capable of intelligent thought. If ( 40 % ) of all aliens are capable of intelligent thought, what percent of aliens have more than 3 arms? ( mathbf{A} cdot 60 ) B. 70 c. 40 D. 45 | 11 |

114 | Write all the subsets of the sets ( (i){a} ) ( (i i) phi ) | 11 |

115 | If ( A ) and ( B ) be two sets containing 4 and 8 elements respectively, what can be the maximum number of elements in ( A cup B ? ) Find also, the minimum number of elements in ( (boldsymbol{A} cup boldsymbol{B}) ) ? A. Maximum number of elements ( =12 ) Minimum number of elements = 8 B. Maximum number of elements ( =14 ) Minimum number of elements ( =8 ) c. Maximum number of elements ( =12 ) Minimum number of elements = 9 D. Maximum number of elements ( =14 ) Minimum number of elements ( =7 ) | 11 |

116 | Find ( A triangle B ) and draw Venn diagram when: ( boldsymbol{A}={mathbf{1}, mathbf{2}, mathbf{3}, mathbf{4}, mathbf{5}} ) and ( boldsymbol{B}={mathbf{2}, mathbf{4}} ) | 11 |

117 | Let ( boldsymbol{A}={mathbf{3}, mathbf{6}, mathbf{1 2}, mathbf{1 5}, mathbf{1 8}, mathbf{2 1}}, boldsymbol{B}= ) ( {mathbf{4}, mathbf{8}, mathbf{1 2}, mathbf{1 6}, mathbf{2 0}}, boldsymbol{C}= ) ( {mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}, mathbf{1 2}, mathbf{1 4}, mathbf{1 6}} ) and ( boldsymbol{D}= ) ( {mathbf{5}, mathbf{1 0}, mathbf{1 5}, mathbf{2 0}} . ) Find ( boldsymbol{A}-boldsymbol{D} ) | 11 |

118 | If ( boldsymbol{A}=left{boldsymbol{x} in boldsymbol{R}: boldsymbol{x}^{2}+boldsymbol{6} boldsymbol{x}-boldsymbol{7}<mathbf{0}right} ) and ( boldsymbol{B}=left{boldsymbol{x} in boldsymbol{R}: boldsymbol{x}^{2}+boldsymbol{9} boldsymbol{x}+mathbf{1 4}<mathbf{0}right}, ) then which of the following is/are correct? 1. ( (boldsymbol{A} cap boldsymbol{B})=(-mathbf{2}, mathbf{1}) ) 2. ( (boldsymbol{A} backslash boldsymbol{B})=(-mathbf{7},-mathbf{2}) ) Select the correct answer using the code given below: A. 1 only B. 2 only c. Both 1 and 2 D. Neither 1 nor 2 | 11 |

119 | In a town of 10,000 families it was found that ( 40 % ) families buy newspaper A, ( 20 % ) families buy newspaper ( B ) and 10 ( % ) families buy newspaper ( C .5 % ) families buy A and B, 3% buy B and C and ( 4 % ) buy ( A ) and ( C . ) If ( 2 % ) families buy all the three newspaper, the member of families which buy A only is | 11 |

120 | Which of the following venn-diagrams best represents the sets of females, mothers and doctors? ( A ) B. ( c ) D. | 11 |

121 | Let ( boldsymbol{A}={mathbf{3}, mathbf{6}, mathbf{1 2}, mathbf{1 5}, mathbf{1 8}, mathbf{2 1}}, boldsymbol{B}= ) ( {mathbf{4}, mathbf{8}, mathbf{1 2}, mathbf{1 6}, mathbf{2 0}}, boldsymbol{C}= ) ( {mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}, mathbf{1 2}, mathbf{1 4}, mathbf{1 6}} ) and ( boldsymbol{D}= ) ( {mathbf{5}, mathbf{1 0}, mathbf{1 5}, mathbf{2 0}} . ) Find ( boldsymbol{A}-boldsymbol{C} ) | 11 |

122 | The Venn diagram shows sets ( P, Q ) and ( R ) with regions labelled, I, II, III and IV. State the region which represents set ( left[boldsymbol{P} cap(boldsymbol{Q} cup boldsymbol{R})^{prime}right] ) ( A ) B. ( c . | ) D. IV | 11 |

123 | Define infinite set Is ( {x: x in R: 1 leq x leq 3} ) a infinite set? A. True B. False | 11 |

124 | If ( boldsymbol{A}={boldsymbol{x}: boldsymbol{x} boldsymbol{epsilon} boldsymbol{W}, boldsymbol{3} leq boldsymbol{x}<mathbf{6}}, boldsymbol{B}= ) {3,5,7} and ( C={2,4} ) find ( : boldsymbol{A} times(boldsymbol{B}-boldsymbol{C}) ) Find the number of elements in such a set. | 11 |

125 | ( f(1,2,3,4,5}, B={3,4,7,8} ) then find ( A cup ) ( B ) and ( A cap B ) | 11 |

126 | State whether the following statement is True or False If ( boldsymbol{U}={mathbf{1}, mathbf{2}, mathbf{3}, mathbf{4}, mathbf{5}, mathbf{6}, mathbf{7}} ) and ( boldsymbol{A}= ) ( {5,6,7}, ) then ( U ) is the subset of ( A ) A. True B. False | 11 |

127 | Given, ( boldsymbol{A}={text { Triangles }}, boldsymbol{B}={ ) Isosceles triangles ( } ) ( C={text { Equilateral triangles }} . ) State whether the following statements are correct or incorrect. Give reasons. ( A subset B ) | 11 |

128 | ( X ) is a set of factors of 24 and ( Y ) is a set of factors of ( 36, ) then find the sets ( X cup ) ( boldsymbol{Y} ) and ( boldsymbol{X} cap boldsymbol{Y} ) | 11 |

129 | In a class of 60 students, 45 students like music, 50 students like dancing, 5 students like neither. Then the number of students in the class who like both music and dancing is A . 35 B. 40 c. 50 D. 55 | 11 |

130 | In a group of 15,7 have studied German, 8 have studied French, and 3 have not studied either. How many of these have studied both German and French? A . 0 B. 3 ( c cdot 4 ) D. 5 | 11 |

131 | Which of the following sets is not a finite set? ( mathbf{A} cdotleft{(x, y): x^{2}+y^{2} leq 1 leq x+y, quad x, y in Rright} ) B ( cdotleft{(x, y): x^{2}+y^{2} leq 1 leq x+y, quad x, y in Zright} ) ( mathbf{c} cdotleft{(x, y): x^{2} leq y leq|x|, quad x, y in Zright} ) D. ( left{(x, y): x^{2}+y^{2}=1, x, y in Zright} ) | 11 |

132 | Let ( S ) be the set of all values of ( x ) such ( operatorname{that} log _{2 x}left(x^{2}+5 x+6right)<1 ) then the sum of all integral value of ( x ) in the set S, is ( A cdot O ) B. 8 ( c cdot s ) D. 10 | 11 |

133 | If ( A, B ) and ( C ) are three finite sets then what is ( [(boldsymbol{A} cup boldsymbol{B}) cap boldsymbol{C}]^{prime} ) equal to? A ( cdotleft(A^{prime} cup B^{prime}right) cap C^{prime} ) B ( cdot A^{prime} capleft(B^{prime} cap C^{prime}right) ) c. ( left(A^{prime} cap B^{prime}right) cup C^{prime} ) D. ( (A cap B) cap C ) | 11 |

134 | Draw Venn diagrams to illustrate ( boldsymbol{C} cap ) ( (B backslash A) ) | 11 |

135 | The following sets are equal. ( boldsymbol{A}={boldsymbol{x}: boldsymbol{x} in boldsymbol{N} ; mathbf{1}<boldsymbol{x}<mathbf{4}} ) and ( B=left{x: x text { is a solution of } x^{2}+5 x+right. ) ( mathbf{6}=mathbf{0}} ) A . True B. False | 11 |

136 | f ( A={a, b}, B={x, y} ) and ( C= ) ( {a, c, y}, ) then verify that ( A times ) ( (boldsymbol{B} cap boldsymbol{C})=(boldsymbol{A} times boldsymbol{B}) cap(boldsymbol{A} times boldsymbol{C}) ) | 11 |

137 | State true or false: A set of rational number is a subset of a set of real numbers A. True B. False | 11 |

138 | The Venn diagram shows sets ( boldsymbol{xi}, mathrm{P} ) and ( Q ) The shaded region in the Venn diagram represents set: ( A cdot P cap Q ) в. ( P^{prime} cap Q ) c. ( P cap Q^{prime} ) D. ( P^{prime} cap Q^{prime} ) | 11 |

139 | If a set contains ( n ) elements then number of elements in its power set is A ( cdot 2^{n}-n ) B . ( 2^{n}-2 ) ( c cdot 2^{n} ) ( mathbf{D} cdot n^{2} ) | 11 |

140 | If ( boldsymbol{A}=left{4^{n}-3 n-1: n in Nright} ) and ( B= ) ( {9(n-1): n in N}, ) then? ( mathbf{A} cdot B subset A ) B. ( A cup B=N ) c. ( A subset B ) D. None of these | 11 |

141 | ( A subset B ) then show that ( A cap B ) and ( A backslash ) ( B ) (use Venn diagram) | 11 |

142 | Suppose ( boldsymbol{U}= ) ( {3,4,5,6,7,8,9,10,11,12,13}, A= ) ( {3,4,5,6,9}, B={3,7,9,5} ) and ( C= ) ( {6,8,10,12,7} . ) Write down the following set and draw Venn diagram for ( boldsymbol{B}^{prime} ) | 11 |

143 | Looking at the Venn diagram list the elements of the following sets: ( boldsymbol{B} backslash boldsymbol{C} ) | 11 |

144 | If ( boldsymbol{P}={boldsymbol{x} mid mathbf{2 4}<boldsymbol{x}<mathbf{3 0}} ) and ( boldsymbol{Q}= ) ( {boldsymbol{x} mid mathbf{2 5}<boldsymbol{x}<mathbf{3 2}}, ) prove that ( boldsymbol{P}-boldsymbol{Q} neq ) ( boldsymbol{Q}-boldsymbol{P} ) | 11 |

145 | If ( A, B ) and ( C ) are three sets such that ( boldsymbol{A} cap boldsymbol{B}=boldsymbol{A} cap boldsymbol{C} ) and ( boldsymbol{A} cup boldsymbol{B}=boldsymbol{A} cup boldsymbol{C} ) then A ( . A=C ) B. ( B=C ) c. ( A cap B=phi ) D. ( A=B ) | 11 |

146 | Find union of ( A ) and ( B ), and represent it using Venn diagram: ( boldsymbol{A}={mathbf{1}, mathbf{2}, mathbf{3}}, boldsymbol{B}={mathbf{4}, mathbf{5}, mathbf{6}} ) | 11 |

147 | Find the following set is singleton set or not. ( mathrm{B}={boldsymbol{y}: 2 boldsymbol{y}+1<3 text { and } boldsymbol{Y} boldsymbol{epsilon} boldsymbol{W}} ) | 11 |

148 | Find union of ( A ) and ( B ) by representing using Venn diagram: ( boldsymbol{A}={boldsymbol{a}, boldsymbol{b}, boldsymbol{c}, boldsymbol{d}}, boldsymbol{B}={boldsymbol{b}, boldsymbol{d}, boldsymbol{e}, boldsymbol{f}} ) ( mathbf{A} cdot{a, b, c, d} ) B ( cdot{b, d, e, f} ) ( mathbf{c} cdot{b, d} ) D. None of these | 11 |

149 | ( 40 % ) of all high school students hate roller coasters; the rest love them. ( 20 % ) of those students who love roller coasters own chinchillas. What percentage of students love roller coasters but do not own a chinchilla? A . 45 B . 30 c. 50 D. 48 | 11 |

150 | Let ( n(cup)=700, n(A)=400, n(B)=300, n(A cap ) ( mathrm{B})=300 . ) Then ( left(mathrm{A}^{prime} cap mathrm{B}^{prime}right)= ) A . 300 B. 400 ( c . ) 350 D. 250 | 11 |

151 | How many took ‘soup’ | 11 |

152 | Stat whether the following pairs of sets are equal or not (I) ( A={x: x text { is a letter of the world ‘paper’ }} ) and ( A=operatorname{set} ) of digits in the number 59672 (ii) ( A={x: x text { is a letter of the world ‘pepar’ }} ) and ( mathrm{B}=operatorname{set} ) of digits in the number 756889 | 11 |

153 | Find ( A triangle B ) and draw Venn diagram when: ( boldsymbol{A}={boldsymbol{a}, boldsymbol{b}, boldsymbol{c}, boldsymbol{d}} ) and ( boldsymbol{B}={boldsymbol{d}, boldsymbol{e}, boldsymbol{f}} ) | 11 |

154 | The Venn diagram shows sets ( xi, P ) and ( Q ) The shaded region in the Venn diagram represents set ( A cdot P cap Q ) в. ( P^{prime} cap Q ) c. ( P cap Q^{prime} ) D. ( P^{prime} cap Q^{prime} ) | 11 |

155 | Let ( A, B, C ) be the subsets of the universal set ( X ) Let ( A^{prime} B^{prime} C^{prime} ) denote their complements in X Then which of below corresponds to the shaded portion in the given figure ( mathbf{A} cdot A^{prime} cap B cap C ) B ( cdot A cap B^{prime} cap C ) c. ( A cap B cap C^{prime} ) ( mathbf{D} cdot A^{prime} cap B^{prime} cap C ) | 11 |

156 | ( P, Q ) and ( R ) are three sets and ( xi P cup Q cup ) ( R . ) Given that ( n(xi)=60, n(P cap Q)=5 ) ( n(Q cap R)=10, n(p)=20 ) and ( n(Q)=23 ) find ( nleft(P^{prime} cup Qright) ) A. 37 3. 38 ( c cdot 45 ) D. 52 | 11 |

157 | Find ( A triangle B ) and draw Venn diagram when: ( boldsymbol{A}={1,4,7,8} ) and ( boldsymbol{B}={4,8,6,9} ) | 11 |

158 | State whether the following statement is True or False ( A={x mid x text { is a negative integer } ; x> ) -5} is a finite set. A. True B. False | 11 |

159 | Draw Venn diagrams to illustrate ( (boldsymbol{A} cup ) ( boldsymbol{B}) backslash(boldsymbol{A} cup boldsymbol{C}) ) | 11 |

160 | Draw Venn diagrams to illustrate ( boldsymbol{C} cap ) ( (boldsymbol{B} cup boldsymbol{A}) ) | 11 |

161 | The shaded part of the given figure is represented as ( A cdot A cap B ) в. ( A cup B ) ( c cdot A-B ) D. All of the above | 11 |

162 | If the following statement is true, enter 1 or else 0. The set of even natural numbers less | 11 |

163 | 8. Let P = {0: sin 0 — cos 0 – 2 cos) and Q= {0: sin + cos 0 – 2 sin 0; be two sets. Then (2011) (a) P Q and 0-P (b) P (c) P Q (d) P=0 | 11 |

164 | Draw Venn diagrams to illustrate ( boldsymbol{A} cap ) ( (B backslash C) ) | 11 |

165 | The set of letters needed to spel “CATARACT” and the set of letter needed to spell “TRACT” are equal A. True B. False | 11 |

166 | Let ( n ) be a natural number and ( X= ) ( {1,2, dots dots, n} . ) For subsets ( A ) and ( B ) of ( X, ) we denote ( A Delta B ) to be the set of all those elements of ( X ) which belong to exactly one of ( A ) and ( B . ) Let ( F ) be a collection of subsets of ( X ) such that for any two distinct elements ( A ) and ( B ) in ( F ) the ( operatorname{set} A Delta B ) has at least two elements. Show that ( F ) has at most ( 2^{n-1} ) elements Find all such collections ( boldsymbol{F} ) with ( mathbf{2}^{n-1} ) elements. | 11 |

167 | If ( boldsymbol{X}={1,2,3,4,5,6,7,8,9,10} ) is the universal set and ( boldsymbol{A}={1,2,3,4}, B= ) ( {2,4,6,8}, C={3,4,5,6} ) verify the following. (a) ( boldsymbol{A} cup(boldsymbol{B} cup boldsymbol{C})=(boldsymbol{A} cup boldsymbol{B}) cup boldsymbol{C} ) ( (b) A cap(B cup C)=(A cap B) cup(A cap C) ) (c) ( left(boldsymbol{A}^{prime}right)^{prime}=boldsymbol{A} ) A. Only a is true B. Only b and c are true c. only a and b are true D. All three a, b and c are true. | 11 |

168 | Let ( boldsymbol{P}= ) Set of all integral multiples of 3 ( ; Q=operatorname{set} ) of integral multiples of ( 4 ; R= ) Set of all integral multiples of 6 Consider the following relations: ( mathbf{1} boldsymbol{P} cup boldsymbol{Q}=boldsymbol{R} ) ( mathbf{2} . boldsymbol{P} subset boldsymbol{R} ) 3. ( boldsymbol{R} subset(boldsymbol{P} cup boldsymbol{Q}) ) Which of the relations given above is/are correct ? A. only 1 B . only 2 c. only 3 D. both 2 and 3 | 11 |

169 | Let ( boldsymbol{E}=left{boldsymbol{x}: boldsymbol{x}^{2}+mathbf{5} boldsymbol{x}-boldsymbol{6}=boldsymbol{0}right} ) and ( boldsymbol{F}={-mathbf{6}, mathbf{1}} . ) Then A ( . E=F ) в. ( E neq F ) c. ( E subset F ) D. ( F subset E ) | 11 |

170 | Let ( A, B ) are two sets such that ( n(A)= ) ( mathbf{6}, boldsymbol{n}(boldsymbol{B})=mathbf{8} ) then the maximum number of elements in ( n(A cup B) ) is A. 7 B. 9 c. 14 D. None | 11 |

171 | Directions : From among the giv- en alternatives select the one in which the set of numbers is most like the set of numbers given in the question. 10. Given set : (2, 10, 28) (1) (4, 20, 56) (2) (7, 42, 49) (3) (12, 24, 48) (4) (9, 27, 81) | 11 |

172 | State whether the given set is finite or infinite :Enter 1 for Finite and 0 for infinite ( A={x: x in Z text { and } x<10} ) | 11 |

173 | State whether the set is finite or infinite: The set of points on a line | 11 |

174 | The sets ( A={text { letters of the world ‘FLOW’ }} ) and ( mathrm{B}={text { letters of the word ‘FOLLOW’ }} ) are : A. Equivalent sets B. Equal sets c. singleton sets D. Null sets | 11 |

175 | Let ( boldsymbol{A}={1,2,3,4} ) and ( B={2,4,6,8} ) Then find ( boldsymbol{A}-boldsymbol{B} ) | 11 |

176 | Use the given figure to find ( : boldsymbol{n}left(boldsymbol{B}^{prime} cap boldsymbol{A}right) ) Given, ( n(xi)=52, n(A)=43 ) and ( boldsymbol{n}(boldsymbol{B})=mathbf{2 7} ) | 11 |

177 | 8 have studied French and 3 have not studied either. The Venn diagram showing the number of students who have studied both is : ( mathbf{A} ) B. ( c ) ( D ) | 11 |

178 | Which of the following Venn diagrams correctly represents persons, trees and environment? ( A ) B. ( c ) D. | 11 |

179 | In a survey of 100 persons it was found that 28 read magazine ( A, 30 ) read magazine B, 42 read magazine ( C, 8 ) read magazines ( A ) and ( B, 10 ) read magazines A and ( mathrm{C}, 5 ) read magazines ( mathrm{B} ) and ( mathrm{C} ) and 3 read all the three magazines. Find how many read none of three magazines? | 11 |

180 | Classify ( C={ldots,-3,-2,-1,0} ) as ‘finite’ or ‘infinite’. A . Infinite B. Finite c. Data insufficient D. None of these | 11 |

181 | In a battle ( 70 % ) of the combatants lost one eye, ( 80 % ) an ear, ( 75 % ) an arm, ( 85 % ) a leg, ( x % ) lost all the four limbs the minimum value of ( x ) is A . 10 B. 12 c. 15 D. | 11 |

182 | If ( A ) and ( B ) are non-empty sets such that ( A supset B, ) then ( mathbf{A} cdot B^{prime}-A^{prime}=A-B ) B ( cdot B^{prime}-A^{prime}=B-A ) ( mathbf{C} cdot A^{prime}-B^{prime}=A-B ) D ( cdot A^{prime} cap B^{prime}=B-A ) E ( cdot A^{prime} cup B^{prime}=A^{prime}-B^{prime} ) | 11 |

183 | In Venn diagram given: ( mathbf{A} cdot A cup B=0 ) В ( . A cup B=mu ) ( mathbf{c} cdot A cap B=mu ) D. ( A cap B=phi ) | 11 |

184 | Let ( A_{1}, A_{2} ) and ( A_{3} ) be subsets of a set ( X ) Which one of the following is correct? A. ( A_{1} cup A_{2} cup A_{3} ) is the largest subset of ( X ) containing elements of each of ( A_{1}, A_{2} ) and ( A_{3} ) B. ( A_{1} cup A_{2} cup A_{3} ) is the smallest subset of ( X ) containing either ( A_{1} ) or ( A_{2} cup A_{3} ) but not both C. The smallest subset of ( X ) containing ( A_{1} cup A_{2} ) and ( A_{3} ) equals the smallest subset of ( X ) containing both ( A_{1} ) and ( A_{2} cup A_{3} ) only if ( A_{2}=A_{3} ) D. None of these | 11 |

185 | If ( A_{1}, A_{2}, dots, A_{100} ) are sets such that ( boldsymbol{n}left(boldsymbol{A}_{boldsymbol{i}}right)=boldsymbol{i}+boldsymbol{2}, boldsymbol{A}_{1} subset boldsymbol{A}_{2} subset boldsymbol{A}_{3} ldots ldots . . boldsymbol{A}_{100} ) and ( bigcap_{i=3}^{100} A_{i}=A, ) then ( n(A)= ) ( A cdot 3 ) B. 4 ( c .5 ) D. 6 | 11 |

186 | If ( boldsymbol{A}={boldsymbol{x}: boldsymbol{x} boldsymbol{epsilon} boldsymbol{W}, boldsymbol{3} leq boldsymbol{x}<mathbf{6}}, boldsymbol{B}= ) ( {mathbf{3}, boldsymbol{5}, boldsymbol{7}} ) and ( boldsymbol{C}={mathbf{2}, boldsymbol{4}} ) find ( : boldsymbol{n}(boldsymbol{A}-boldsymbol{B}) ) | 11 |

187 | In a town of 10000 families, it was found that ( 40 % ) families buy a newspaper ( A ) ( 20 % ) families buy newspaper ( B ) and ( 10 % ) families buy newspaper C. 5% families buy both ( A ) and ( B, 3 % ) buy ( B ) and ( C ) and 4% buy A and C. If 2% families buy all the three newspapers, then the number of families which buy A only. A . 3300 в. 3500 ( c .3600 ) D. 3700 | 11 |

188 | Which of the following is a singleton set? A. ( {x:|x|=5, x in N} ) B . ( {x:|x|=6, x in Z} ) c. ( left(x: x^{2}+2 x+1=0, x in Nright) ) D. ( left{x: x^{2}=7, x in Nright} ) | 11 |

189 | Mark the correct alternative of the following. For any ( operatorname{set} A,left(A^{prime}right)^{prime} ) is equal to? A ( cdot A^{prime} ) B. A ( c cdot phi ) D. None of these | 11 |

190 | Find union of ( A ) and ( B ) by representing using Venn diagram: ( boldsymbol{A}={1,2,3,4,8,9}, B={1,2,3,5} ) ( mathbf{A} cdot{1,2,3,4,5,8,9} ) B . {1,2,3} ( mathbf{c} cdot{1,2,3,4,8,9} ) D. None of these | 11 |

191 | sets of students who have opted for Mathematics (M) physics (P) Chemistry (C) and Electronics (E) What does the shaded region represent A. Students who oped for Physic, Chemistry and Electronics B. Students who oped for Mathematics, Physics Chemistry c. Students who opted for Mathematics, Physics and Electronics D. Students who opted for Mathematics, Chemistry and ectron | 11 |

192 | Use the given figure to find : Given, ( n(xi)=52, n(A)=43 ) and ( boldsymbol{n}(boldsymbol{B})=mathbf{2 7} ) ( nleft(B^{prime}right) ) | 11 |

193 | From a survey of 100 college students, a marketing research company found that 75 students owned stereos, 45 owned cars, and 35 owned cars and stereos. How many students owned either a car or a stereo? A . 85 B. 47 ( c .68 ) D. None of these | 11 |

194 | ( boldsymbol{n}(boldsymbol{A} cap boldsymbol{B}) ) | 11 |

195 | In a group of 1000 people, there are 750 who can speak Hindi and 400 who can speak Bengali. How many can speak Bengali ? | 11 |

196 | Say true or false: ( mathrm{C}={text { even numbers between } 6 text { and } 10} ) is not an empty set. A. True B. False | 11 |

197 | Find the intersection of ( boldsymbol{A} ) and ( boldsymbol{B}, ) and represent it by Venn diagram: ( boldsymbol{A}={1,2,4,5}, B={2,5,7,9} ) | 11 |

198 | State whether the following sets are finite or infinite (i) ( A={x: x text { is a multiple of } 5, x in mathbb{N}} ) (ii) ( B={x: x ) is an even prime number (iii) The set of all positive integers greater than 50 | 11 |

199 | f ( boldsymbol{A}=(boldsymbol{6}, boldsymbol{7}, boldsymbol{8}, boldsymbol{9}), boldsymbol{B}=(boldsymbol{4}, boldsymbol{6}, boldsymbol{8}, boldsymbol{1} boldsymbol{0}) ) and ( C={x: x in N: 2<x leq 7} ; ) find : ( boldsymbol{B}-(boldsymbol{A} cap boldsymbol{C}) ) The sum of the elements in the above ( operatorname{set} ) is? | 11 |

200 | What does the shaded region represent in the figure given below? A ( cdot(P cup Q)-(P cap Q) ) В . ( P cap(Q cup R) ) ( mathbf{c} cdot(P cap Q) cap(P cap R) ) D ( cdot(P cap Q) cup(P cap R) ) | 11 |

201 | Draw Venn diagrams to illustrate ( boldsymbol{A} cap ) ( B^{prime} ) | 11 |

202 | Let ( boldsymbol{A}={boldsymbol{x}: boldsymbol{x} in boldsymbol{N}, mathbf{1}<boldsymbol{x} leq mathbf{3}} ) and ( boldsymbol{B}=left{boldsymbol{y}: boldsymbol{y}^{2}-mathbf{5} boldsymbol{y}+boldsymbol{6}=mathbf{0}right}, ) then A ( . A subset B ) в. ( B subset A ) ( mathbf{c} cdot A=B ) D. ( A neq B ) | 11 |

203 | The set of all values of ( ^{prime} x^{prime} ) satisfying the inequation ( left(frac{1}{|x|-3}right) leq frac{1}{2} ) is A ( (-infty,-5) cup(-3,3) cup[5, infty) ) B . ( (-infty,-5] cup[-3,3] cup[5, infty) ) c. ( (-infty,-5) cup(-3,3) cup(5, infty) ) D. None of the above | 11 |

204 | If universal set ( boldsymbol{xi}= ) ( {a, b, c, d, e, f, g, h}, A= ) ( {b, c, d, e, f}, B={a, b, c, g, h} ) and ( C={c, d, e, f, g}, ) then find ( B-A ) ( mathbf{A} cdot{b, c, e, f} ) в. ( {a, b, f, h} ) ( c cdot{a, g, h} ) D. ( {a, c, e, g} ) | 11 |

205 | Given the set ( P ) is the set of even numbers between 15 and ( 25 . ) Label a Venn diagram to represent the set ( boldsymbol{P} ) and indicate all the elements of set ( boldsymbol{P} ) in the Venn diagram. B . {16,20,24} c. {16,18,20,22,24} D. None of these | 11 |

206 | f ( x={a, b, c, d} ) and ( y={b, d, g, f} ) find ( boldsymbol{x}-boldsymbol{y} ) and ( boldsymbol{y}-boldsymbol{x} ) Draw the appropriate venn diagram for ( boldsymbol{A}^{prime} cap boldsymbol{B}^{prime} ) | 11 |

207 | Eighty-nine students of class VIII appeared for a combined test in Maths and Physics. If 62 students passed in both ( ; 4 ) failed in Maths and Physics and 7 failed only in Maths. Use a Venndiagram to find: how many passed in Maths. | 11 |

208 | Draw Venn diagrams to illustrate ( (A cup ) ( B)^{prime} ) | 11 |

209 | If ( A ) and ( B ) are two disjoint sets and ( N ) is universal set, then ( boldsymbol{A}^{circ} cupleft[(boldsymbol{A} cup boldsymbol{B}) cap boldsymbol{B}^{circ}right] ) is ( A cdot phi ) в. ( A ) ( c . B ) D. ( N ) | 11 |

210 | 000 0 0 ( infty ) 00 | 11 |

211 | From the diagram, relation between ( A ) and B……. | 11 |

212 | If ( boldsymbol{A}=left{(boldsymbol{x}, boldsymbol{y}) mid boldsymbol{x}^{2}+boldsymbol{y}^{2} leq mathbf{4}right} ) and ( boldsymbol{B}= ) ( left{(x, y) mid(x-3)^{2}+y^{2} leq 4right} ) and the point ( Pleft(a, a-frac{1}{2}right) ) belongs to the set ( B-A, ) then the set of possible real values of ( a ) is ( ^{mathrm{A}} cdotleft(frac{1+sqrt{31}}{4}, frac{7+sqrt{7}}{4}right] ) в. ( left[frac{7-sqrt{7}}{4}, frac{1+sqrt{31}}{4}right) ) ( ^{c} cdotleft(frac{1-sqrt{31}}{4}, frac{7-sqrt{7}}{4}right] ) D. None of the above | 11 |

213 | The number of subsets of the set {10,11,12} is ( A cdot 3 ) B. 8 ( c cdot 6 ) D. 7 | 11 |

214 | Let ( boldsymbol{A}={-mathbf{7}, mathbf{5}, mathbf{2}} ) and ( boldsymbol{B}= ) ( {sqrt[3]{125}, sqrt{4}, sqrt{49}} ) Are the sets ( A ) and ( B ) equal? Choose the correct option for the above. Justify your answer. A. Yes B. No c. Ambiguous D. Data insufficient | 11 |

215 | begin{tabular}{l} ( infty ) \ hline 00 \ hline 0 \ hline( infty ) end{tabular} | 11 |

216 | In a group of 15 women, 7 have nose studs, 8 have ear rings and 3 have neither. How many of these have both nose studs and ear rings? A . 0 B . 2 ( c .3 ) D. | 11 |

217 | Given ( A={x: x in N text { and } 3<x leq 6} ) and ( mathrm{B}={x: x in W text { and } x<4}, ) then find ( : A-B ) | 11 |

218 | The numbers representing ( boldsymbol{A} cap boldsymbol{B} ) are | 11 |

219 | ( P cup Q ) and ( P cap Q ) | 11 |

220 | The number of subsets ( boldsymbol{R} ) of ( boldsymbol{P}= ) ( (1,2,3, dots, 9) ) which satisfies the property “There exit integers ( mathbf{a} in mathbf{R}, mathbf{b} in ) ( mathbf{R}, mathbf{c} in mathbf{R}^{prime prime} ) is A .512 в. 466 c. 467 D. None of these | 11 |

221 | An investigator interviewed 100 students to determine their preferences for the three drinks milk coffee and tea. He reported the following, 10 students had all the three drinks, 20 had milk and coffee, 30 had coffee and tea ( , 25 ) had milk and tea, 12 had milk only. 5 had coffee only, 8 had tea only. The number of students that did not take any of the three drinks is. | 11 |

222 | Is ( A^{prime} cup B^{prime}=(A cap B)^{prime} ) ? Also, verify if ( A^{prime} cap B^{prime} ) ( =(A cup B)^{prime} ) A. Yes B. No ( c ). Can’t Say D. Cannot be determined | 11 |

223 | ( (boldsymbol{P} cap boldsymbol{Q}) cup(boldsymbol{Q} cap boldsymbol{R}) ) A ( cdot{b, c, f} ) в. ( {b, c, d} ) ( mathbf{c} cdot{b, c, d, f} ) ( mathbf{D} cdot{b, c, f, g} ) | 11 |

224 | For any three sets, ( A B ) and ( C, B backslash(A cup ) ( C) ) is: ( mathbf{A} cdot(A backslash B) cap(A backslash C) ) B . ( (B backslash A) cap(B backslash C) ) c. ( (B backslash A) cap(A backslash C) ) D. ( (A backslash B) cap(B backslash C) ) | 11 |

225 | ( mathbf{f} boldsymbol{A}={mathbf{6}, mathbf{9}, mathbf{1 1}} ) and ( boldsymbol{B}=boldsymbol{phi} ),find ( boldsymbol{A} cup boldsymbol{B} ) | 11 |

226 | ( A ) and ( B ) are two sets having 3 elements in common.ff ( n(mathbf{A})=mathbf{5}, n(mathbf{B})=mathbf{4} ) then Find ( boldsymbol{n}(boldsymbol{A} times boldsymbol{B}) boldsymbol{a} boldsymbol{n} boldsymbol{d} boldsymbol{n}[(boldsymbol{A} times boldsymbol{B}) cap(boldsymbol{B} times boldsymbol{A})] ) | 11 |

227 | Find total number of subsets of ( A={5,7} ) | 11 |

228 | ( operatorname{Set} boldsymbol{U}={1,2, mathbf{3}, mathbf{4}, mathbf{5}, mathbf{6}, mathbf{7}, mathbf{8}, mathbf{9}}, boldsymbol{A}= ) ( left{x: x in N, 30 leq x^{2} leq 70right}, B={x: x ) is a prime number ( <10} . ) Which of the following does NOT belong to the set ( (A-B)^{prime} ? ) ( mathbf{A} cdot mathbf{4} ) B. 5 ( c cdot 6 ) D. | 11 |

229 | Which of the following are examples of the null Set of all even prime numbers. A. True B. False | 11 |

230 | List all of the subsets of the set ( {a, b, c, d} ) | 11 |

231 | Using properties of sets, prove that ( boldsymbol{A} cup ) ( (boldsymbol{A} cap boldsymbol{B})=boldsymbol{A} ) | 11 |

232 | Use the Venn diagram to answer the following questions (i) List ( U, G ) and ( H ) (ii) Find ( G^{prime}, H^{prime}, G^{prime} cap H^{prime}, n(G cup H)^{prime} ) and ( boldsymbol{n}(boldsymbol{G} cap boldsymbol{H})^{prime} ) | 11 |

233 | Write down the set represented by the shaded region in figure (ii) | 11 |

234 | The Venn diagram shows the sets ( xi, P, Q ) and ( R . ) Which of the following is not true? ( mathbf{A} cdot P cap Q neq emptyset ) в. ( R subset Q ) ( mathbf{c} cdot(P cap R) subset Q ) D. ( (P cap Q)=R ) | 11 |

235 | In the Venn diagram, the numbers represent the number of elements in the subsets. Given that ( boldsymbol{xi}=boldsymbol{F} cup boldsymbol{G} cup boldsymbol{H} ) and ( boldsymbol{n}(boldsymbol{xi})=mathbf{4 2}, ) find ( nleft(G^{prime} cup Hright) ) ( A cdot 18 ) 3. 28 ( c .30 ) 0.38 | 11 |

236 | Use Venn diagrams to verify De’Morgan’s law of complementation ( (boldsymbol{A} cup boldsymbol{B})^{prime}=boldsymbol{A}^{prime} cup boldsymbol{B}^{prime} ) | 11 |

237 | Is the following statement True or False? ( (boldsymbol{A}-boldsymbol{B}) cup(boldsymbol{B}-boldsymbol{A})=(boldsymbol{A} cup boldsymbol{B}) cap ) ( left(A^{prime} cup B^{prime}right) ) If True then write answer as 1 If False then write answer as 0 | 11 |

238 | If ( boldsymbol{T}= ) ( {x: x text { is a letter in the word ‘TEETH’ }} ) find all its subsets. | 11 |

239 | Find ( n(B-C)^{c} ) | 11 |

240 | If ( X ) and ( Y ) are two sets, then ( X cap(Y cup ) ( X)^{prime} ) equals ( mathbf{A} cdot X ) в. ( Y ) ( c cdot phi ) D. None of these | 11 |

241 | Let ( P ) be the set of points inside the square, ( Q ) be the set of points inside the triangle and ( R ) be the set of points inside the circle. If the triangle and circle intersect each other and are contained in the square then, This question has multiple correct options A. ( P cap Q cap R neq phi ) в. ( P cup Q cup R=R ) c. ( P cup Q cup R=P ) D. ( P cup Q=R cup P ) | 11 |

242 | If ( boldsymbol{A}={boldsymbol{x}: boldsymbol{x} in boldsymbol{W}, boldsymbol{3} leq boldsymbol{x}<mathbf{6}}, boldsymbol{B}= ) ( {boldsymbol{3}, boldsymbol{5}, boldsymbol{7}} ) and ( boldsymbol{C}={mathbf{2}, boldsymbol{4}} ; ) find : ( boldsymbol{B}-boldsymbol{C} ) | 11 |

243 | There are 60 students in a class. Every student learns at least one of the subjects Kannada or English. 45 students offer Kannada and 30 English. How many students offer both the subjects? Draw Venn diagram. | 11 |

244 | If universal set ( boldsymbol{xi}= ) ( {boldsymbol{a}, boldsymbol{b}, boldsymbol{c}, boldsymbol{d}, boldsymbol{e}, boldsymbol{f}, boldsymbol{g}, boldsymbol{h}}, boldsymbol{A}= ) ( {b, c, d, e, f}, B={a, b, c, g, h} ) and ( boldsymbol{C}={boldsymbol{c}, boldsymbol{d}, boldsymbol{e}, boldsymbol{f}, boldsymbol{g}} ) find ( : boldsymbol{C}-(boldsymbol{B} cap boldsymbol{A}) ) Thus find the number of elements in the above set. | 11 |

245 | fin ( (A)=120, N(B)=250 ) and ( n(A-B)= ) 52, then find ( n(A cup B) ) A . 302 B. 250 ( c .368 ) D. None of the above | 11 |

246 | Examine whether ( boldsymbol{A}={boldsymbol{x}: boldsymbol{x} ) is a positive integer divisible by ( 3} ) is a subset of ( B={x: x text { is a multiple of } 5 ) ( boldsymbol{x} in boldsymbol{N}} ) | 11 |

247 | Use the given Venn-diagram to find: B – 4 3. 10 ( c ) P | 11 |

248 | The Venn diagram shows the relationship between sets ( xi, P, Q ) and ( R ) The shaded region in the diagram represents set: ( A cdot(P cap R) cap Q ) B . ( left(P cap R^{prime}right) cap Q^{prime} ) ( mathrm{c} cdotleft(P cap R^{prime}right) cap Q ) ( mathrm{D} cdot Q^{prime} cap R^{prime} ) | 11 |

249 | 00 00 00 00 | 11 |

250 | State whether the set is finite or infinite: The set of all schools in this world | 11 |

251 | If ( boldsymbol{A}=(mathbf{6}, mathbf{7}, mathbf{8}, mathbf{9}), boldsymbol{B}=(mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}) ) and ( C={x: x in N: 2<x leq 7} ; ) find : ( boldsymbol{B}-boldsymbol{B} ) ( A cdot phi ) B . {0} c. {6,7} D. {4} | 11 |

252 | Let ( boldsymbol{A}={mathbf{1}, mathbf{2}, mathbf{3}, mathbf{4}, mathbf{5}, mathbf{6}}, boldsymbol{B}={mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}} ) Find ( boldsymbol{A}-boldsymbol{B} ) and ( boldsymbol{B}-boldsymbol{A} ) | 11 |

253 | The following is an example of empty set: ( {x: x ) is a point common to any two parallel lines A. True B. False | 11 |

254 | If ( A ) has 2 elements and ( B ) has 2 elements, then the number of elements ( operatorname{in} B times A ) is : | 11 |

255 | If ( boldsymbol{A}={mathbf{2}, mathbf{4}{mathbf{5}, mathbf{6}}, mathbf{8}}, ) then which one of the following statements is not correct? ( mathbf{A} cdot{5,6} subseteq A ) ( mathbf{B} cdot{5,6} in A ) c. {2,4,8}( subseteq A ) D. ( 2,4,8 in A ) | 11 |

256 | Prove that: ( 1 . P(1,1)+2 . P(2,2)+ ) ( 3 . P(3,3)+ldots+n . P(n, n)= ) ( P(n+1, n+1)-1 ) | 11 |

257 | Let ( boldsymbol{A}={1,2,3, dots, 10} ) and ( B= ) ( {101,102,103, dots, 1000} . ) Then set ( A ) and ( B ) are A. Both finite sets B. Infinite and finite set respectively c. Both Infinite sets D. Finite and infinite set respectively | 11 |

258 | f ( M={b, h, i} ; N={b, c, d, e} ) and ( s={e, f, g}, ) determine ( M cap N cap S ) and represent it in a venn diagram. | 11 |

259 | The ( (boldsymbol{A} cup boldsymbol{B} cup boldsymbol{C}) capleft(boldsymbol{A} cap boldsymbol{B}^{C} cap boldsymbol{C}^{C}right)^{C} cap ) ( C^{c} ) is equal to ( mathbf{A} cdot B^{C} cap C^{C} ) в. ( A cap C ) ( c cdot B cap C^{c} ) D. ( C cap C^{c} ) | 11 |

260 | f ( A=1,3,5, dots dots dots 17 ) and ( B= ) ( 2,4,6, dots dots 18 ) and ( N( ) the set of natural numbers) is the universal set, then show that ( boldsymbol{A}^{prime} cupleft((boldsymbol{A} cup boldsymbol{B}) cap boldsymbol{B}^{prime}right)=boldsymbol{N} ) | 11 |

261 | If ( boldsymbol{A}={mathbf{2}, mathbf{3}, mathbf{4}, mathbf{5}, mathbf{7}, mathbf{9}}, boldsymbol{B}= ) ( {mathbf{2}, mathbf{3}, mathbf{4}, mathbf{5}, mathbf{6}} ) then ( boldsymbol{B}-boldsymbol{A}= ) | 11 |

262 | If ( A subset B ) then show that ( A cup B=B ) (use Venn diagram) | 11 |

263 | Classify ( B={y mid y text { is a factor of } 13} ) as ‘finite’ or ‘infinite’. A . Infinite B. Finite c. Data insufficient D. None of these | 11 |

264 | Statements (i) Some chalks are chairs (ii) Some chairs are tables. Conclusions: I. Some chalks are tables. II. Some tables are chalks. A. Only conclusion lis true B. Only conclusion II is true c. Both conclusions I and II are true D. Neither conclusion I nor conclusion II is true | 11 |

265 | Let ( boldsymbol{A}={mathbf{3}, mathbf{6}, mathbf{1 2}, mathbf{1 5}, mathbf{1 8}, mathbf{2 1}}, boldsymbol{B}= ) ( {mathbf{4}, mathbf{8}, mathbf{1 2}, mathbf{1 6}, mathbf{2 0}}, boldsymbol{C}= ) ( {mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}, mathbf{1 2}, mathbf{1 4}, mathbf{1 6}} ) and ( boldsymbol{D}= ) ( {mathbf{5}, mathbf{1 0}, mathbf{1 5}, mathbf{2 0}} . ) Find ( boldsymbol{C}-boldsymbol{A} ) | 11 |

266 | State the following statement is True or False ( boldsymbol{D}=left{boldsymbol{y} mid boldsymbol{y}=boldsymbol{3}^{n}, boldsymbol{n} in boldsymbol{N}right} ) is an example of an infinite set. A. True B. False | 11 |

267 | (0) THU 59. If X = {4″ – 3n-1: neN : neN} and Y = {9(n-1):n € N}, and Ya N is the set of natural numbers, then X UY is equal to: [JEE M 2014) (a) x (6) y (0) N (d) Y-X 1 members is | 11 |

268 | Of 30 applicants for a job, 14 had at least 4 years’experience, 18 had degrees, and 3 had less than 4 years experience and did not have a degree. How many of the applicants had at least 4 years’ experience and a degree? A . 14 B. 13 c. 9 ( D .7 ) E. 5 | 11 |

269 | 6. Let P = {0: sin 0 – cos e = V cos 8; and Q = {0: sin e + cos 0 = V2 sin 8} be two sets. Then a. P(Q and Q-P+º) b. QxP c. PxQ b d. P=Q (IIT-JEE 2011) | 11 |

270 | ( boldsymbol{n}[boldsymbol{P}(boldsymbol{A})]=boldsymbol{n}[boldsymbol{P}(boldsymbol{B})], ) then ( A ) and ( mathrm{B} ) are sets A . Equal B. Overlapping c. Equivalent D. Dissoint | 11 |

271 | ( P, Q ) and ( R ) are three sets and ( xi P cup Q cup ) ( R . ) Given that ( n(xi)=60, n(P cap Q)=5 ) ( n(Q cap R)=10, n(p)=20 ) and ( n(Q)=23 ) find ( nleft(P^{prime} cup Qright) ) A. 37 3. 38 ( c cdot 45 ) D. 52 | 11 |

272 | Thirty percent of the members of a swim club have passed the life saving test. Among the members who have not passed the test, 12 have taken the preparatory course and 30 have not taken the course.How many members are there in the swim club? A . 60 B. 80 ( c .100 ) D. 120 E . 140 | 11 |

273 | ( a, e ) is a subset of ( {x: x ) is a vowel in the English alphabet ( . text { Enter } 1 text { if true or } 0 text { otherwise }) ) | 11 |

274 | If ( boldsymbol{A}={mathbf{1}, mathbf{4}, mathbf{9}, mathbf{1 6}, mathbf{2 5}, dots} ) and ( boldsymbol{B}= ) ( left{boldsymbol{x} mid boldsymbol{x}=boldsymbol{n}^{2}, boldsymbol{n} in boldsymbol{N}right}, ) then A ( . A=B ) в. ( A neq B ) c. ( A subset B ) D. ( B subset A ) | 11 |

275 | Let ( boldsymbol{A}={mathbf{1}, mathbf{3}, mathbf{3}, mathbf{1}} ) and ( boldsymbol{B}={mathbf{1}, boldsymbol{4}} ) then: ( mathbf{A} cdot A neq B ) в. ( A=B ) ( c cdot A subset B ) D. ( B subset A ) | 11 |

276 | If ( X ) and ( Y ) are two sets then ( X cap(Y cup ) ( X)^{prime} ) equals: ( mathbf{A} cdot X ) в. ( Y ) ( c cdot phi ) D. {0} | 11 |

277 | ( boldsymbol{A} cap boldsymbol{X}=boldsymbol{B} cap boldsymbol{X}=boldsymbol{phi} & boldsymbol{A} cup boldsymbol{X}=boldsymbol{B} cup boldsymbol{X} ) prove that ( boldsymbol{A}=boldsymbol{B} ) | 11 |

278 | If ( boldsymbol{A} subset boldsymbol{B}, ) then ( boldsymbol{A} cap boldsymbol{B} ) is A. ( B ) в. ( A backslash B ) ( c . A ) D. ( B backslash A ) | 11 |

279 | In a class of 100 students, 55 students have passed in physics and 67 students have passed in Mathematics. Find the number of students passed in Physics only. | 11 |

280 | Write down all possible subsets of the following set. {0,1} | 11 |

281 | ( operatorname{Let} U={1,2,3,4,5,6,7,8,9}, A= ) ( {1,2,3,4}, B={2,4,6,8} ) and ( C= ) ( {3,4,5,6} . ) Find (i) ( A^{prime}(text { ii }) B^{prime}(text { iii) }(A cup ) ( C)^{prime}(text { iv })(A cup B)^{prime}(v)left(A^{prime}right)^{prime}left(text { vi) }(B-C)^{prime}right. ) | 11 |

282 | Find union of ( A ) and ( B, ) and represent it using Venn diagram: ( boldsymbol{A}={1,2,3,4,8,9}, B={1,2,3,5} ) | 11 |

283 | The shaded region in the given figure is ( mathbf{A} cdot A cap(B cup C) ) в. ( A cup(B cap C) ) ( mathbf{c} cdot A cap(B-C) ) D . ( A-(B cup C) ) | 11 |

284 | The following table shows the percentage of the students of a school who participated in Election and Drawing competitions. Competition Election Drawing | 11 |

285 | The total number of subsets of {1,2,6,7} are? A . 16 B. 8 c. 64 D. 32 | 11 |

286 | ( boldsymbol{A} cup(boldsymbol{B} cap boldsymbol{C})=(boldsymbol{A} cup boldsymbol{B}) cap(boldsymbol{A} cup boldsymbol{C}) ) where ( boldsymbol{A}= ) ( {1,2,4,5}, B{2,3,5,6}, C= ) {4,5,6,7} is ( A cup(B cap C)= ) ( {1,2, a, b, 6} ) Find ( a+b ) | 11 |

287 | ( {y: y ) is a point common to any two paral lel lines 3 is {y:yisapointcommontoanytwoparallel ines ( } ) a null set A . True B. False | 11 |

288 | Let ( A, B ) and ( C ) be the sets such that ( boldsymbol{A} cup boldsymbol{B}=boldsymbol{A} cup boldsymbol{C} ) and ( boldsymbol{A} cap boldsymbol{B}=boldsymbol{A} cap boldsymbol{C} ) Show that ( B=C ) | 11 |

289 | If ( X ) and ( Y ) are two sets, then ( X cap ) ( (boldsymbol{Y} cup boldsymbol{X})^{prime} ) equals ( mathbf{A} cdot X ) в. ( Y ) ( c cdot phi ) D. None of these | 11 |

290 | If ( S ) is any set, then the family of all the subsets of ( S ) is called the power set of ( S ) and it is denoted by ( P(S) . ) Power set of a given set is always non-empty. If ( A ) has n elements, then ( P(A) ) has? | 11 |

291 | Draw the Venn diagram of ( boldsymbol{A} cap boldsymbol{B} ) | 11 |

292 | In a certain town, ( 25 % ) families own a phone and ( 15 % ) own a car, ( 65 % ) families own neither a phone nor a car. 2000 families own both a car and a phone. Consider the following statements in this regard. 1) ( 10 % ) families own both a car and a phone Il) ( 35 % ) families own either a car or a phone III) 40,000 families live in the town. Which of the above statements are correct ? A . ( I & I I ) в. I & III c. II & III D. I,II & III | 11 |

293 | Choose that set of numbers from the option set that is similar to the given ( operatorname{set}{10,15,65} ) B . {124,5,3} c. {95,25,5} D. {168,15,4} | 11 |

294 | Write down all possible subsets of the following set. ( {a} ) | 11 |

295 | ( boldsymbol{A}= ) ( {x: x text { is a perfect square, } x<50, x in lambda ) ( boldsymbol{B}= ) ( {x: x=8 m+1, text { where } m in W, s<5 ) then find ( A cap B ) and display it with Venn diagram. | 11 |

296 | Draw Venn diagrams to illustrate ( (boldsymbol{A} mid ) ( boldsymbol{B}) cup(boldsymbol{A} backslash boldsymbol{C}) ) | 11 |

297 | Which one of the following sets is infinite? A. Set of all integers greater than 5 B. Set ofall integers between ( -10^{10} ) and ( +10^{10} ) C. Set of all prime numbers between 0 and ( 10^{100} ) D. Set of all even prime numbers | 11 |

298 | Choose the correct answer from the alternatives given : From the details, find out the number of rural people who are not educated ( A cdot 28 ) 3. 16 ( c cdot 44 ) 25 | 11 |

299 | State whether the following statement is true or false. Give reason to support your answer. A set can have infinitely many subsets. | 11 |

300 | While preparing the progress reports of the students, the class teacher found that ( 70 % ) of the students passed in Hindi, ( 80 % ) passed in English and only ( 65 % ) passed in both the subjects. Find out the percentage of students who failed in both the subjects. A . ( 15 % ) B. 20% c. ( 30 % ) D. ( 35 % ) | 11 |

301 | ( P, Q ) and ( R ) are three sets and ( xi=P cup ) ( Q cup R ) Given that ( n(xi)=60, n(P cap ) ( Q)=5, n(Q cap R)=10, n(P)=20 ) and ( boldsymbol{n}(boldsymbol{Q})=23, ) find ( boldsymbol{n}(boldsymbol{P} cup boldsymbol{R}) ) A . 37 B . 38 c. 45 D. 52 | 11 |

302 | Find ( A triangle B ) and draw Venn diagram when: ( A={a, b, c, d, e} ) and ( B={a, c, e, g} ) | 11 |

303 | Find ( boldsymbol{n}left(boldsymbol{A} cap boldsymbol{C}^{c}right) ) | 11 |

304 | Find the intersection of ( boldsymbol{A} ) and ( boldsymbol{B}, ) and represent it by Venn diagram: ( boldsymbol{A}={boldsymbol{a}, boldsymbol{c}, boldsymbol{d}, boldsymbol{e}}, boldsymbol{B}={boldsymbol{b}, boldsymbol{d}, boldsymbol{e}, boldsymbol{f}} ) ( mathbf{A} cdot{a, c, d, e} ) B ( cdot{d, e} ) ( mathbf{c} cdot{a, b, c, d, e} ) D. None of these | 11 |

305 | Of the 200 students at College ( T ) majoring in one or more of the sciences, 130 are majoring in chemistry and 150 are majoring in biology. If at least 30 of the students are not majoring in either chemistry or biology, then the number of students majoring in both chemistry and biology could be any number from A. 2020 to 50 B. 40 to 70 c. 50 to 130 D. 110 to 130 E. 110 to 150 | 11 |

306 | If ( A ) and ( B ) be two finite sets such that the total number of subsets of A is 960 more than the total number of subsets of ( mathrm{B}, ) then ( n(A)-n(B) ) (where ( n(x) ) denotes the number of elements in set ( x ) ) is equal to? | 11 |

307 | Draw the appropriate Venn diagram for ( A^{prime} cap B^{prime} ) | 11 |

308 | ( int frac{-sin x}{5+cos x} d x ) | 11 |

309 | If, ( A={5,7}, B={7,5}, ) then ( A ) and ( B ) are A. Equal sets B. Unequal sets c. Null sets D. None of these | 11 |

310 | ( A={x: x ) is a letter of the word ‘paper’ } and ( A=operatorname{set} ) of digists in the number ( mathbf{5 9 6 7 8} ) Sets ( A ) and ( B ) are equal A. True B. False | 11 |

311 | Decide whether sets ( A ) and ( B ) are equal sets or not. ( boldsymbol{A}=mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}, boldsymbol{B}={mathbf{x} mid mathbf{x} ) is a positive even natural number less than 9 | 11 |

312 | Use the Venn diagram to answer the following questions (i) List the elements of ( boldsymbol{U}, boldsymbol{E}, boldsymbol{F}, boldsymbol{E} cup boldsymbol{F} ) and ( boldsymbol{E} cap boldsymbol{F} ) (ii) Find ( n(U), n(E cup F) ) and ( n(E cap F) ) | 11 |

313 | If ( A={1,2,3} B={4,5}, ) then find ( A-B ) ( A cdot{1,4,5} ) B. {1,4,3} ( c cdot{1,2,3} ) ( D cdot{4,5} ) | 11 |

314 | ( boldsymbol{A}-(boldsymbol{B} cup boldsymbol{C}) ) ( mathbf{A} cdot{1,6,7,8} ) в. {3,4,5} ( c cdot{2} ) ( D . ) none | 11 |

315 | From the diagram, relation between ( A ) | 11 |

316 | The following is a example of empty set: Set of all even natural numbers divisible by 5 A . True B. False | 11 |

317 | Find the equivalent set for ( boldsymbol{A}-boldsymbol{B} ) A ( . A cup(A cap B) ) B. B – A c. ( A-(A cap B) ) D. ( A cap B ) | 11 |

318 | In a class consisting of 100 students, 20 know English and 20 do not know Hindi and 10 know neither English nor Hindi. The number of students knowing both Hindi and English is: A. 5 B. 10 c. 15 D. 20 | 11 |

319 | Which of the following sets are finite sets. (i) The sets of months in a year. ( (i i){1,2,3, dots} ) ( (i i i){1,2,3, dots, 99,100} ) ( (i v) ) The set of positive integers greater than 100 . A. ( ( i ) ) and ( (i i i) ) B. (i) only c. ( (i i),(i i i) ) and ( (i v) ) D. (ii) and (iv) | 11 |

320 | Given, ( boldsymbol{A}={text { Quadrilaterals }}, boldsymbol{B}={ ) Rectangles ( }, C={text { Squares }}, D={ ) Rhombuses ( } . ) State whether the following statement is correct or incorrect. Give reasons. ( boldsymbol{D} subset boldsymbol{A} ) | 11 |

321 | Find the following set is singleton set or not. ( A={x: 7 x-3=11} ) | 11 |

322 | f ( n(U)=50, n(A)=20, nleft((A cup B)^{prime}right)=18 ) then ( n(B-A) ) is A . 14 B. 12 c. 16 D. 20 | 11 |

323 | If ( boldsymbol{A}={1,2,3,4}, ) what is the number of subsets of A with at least three elements? ( mathbf{A} cdot mathbf{3} ) B. 4 ( c .5 ) D. 10 | 11 |

324 | Let ( Q ) be a non empty subset of ( N ) and ( q ) is a statement as given below: ( boldsymbol{q}: ) There exists an even number ( boldsymbol{a} in boldsymbol{Q} ) Negation of the statement ( boldsymbol{q} ) will be : A. There is no even number in the set ( Q ) B. Every ( a in Q ) is an odd number c. ( (a) ) and ( (b) ) both D. None of these | 11 |

325 | Given ( boldsymbol{A}={boldsymbol{a}, boldsymbol{b}, boldsymbol{c}, boldsymbol{d}, boldsymbol{e}, boldsymbol{f}, boldsymbol{g}, boldsymbol{h}} ) and ( boldsymbol{B}= ) ( {a, e, i, o, u} ) then ( B-A ) is equal to A ( cdot{i, o, u} ) в. ( {a, b, c} ) c. ( {c, d, e} ) D. ( {a,, i, z} ) | 11 |

326 | 00 0 00 0 | 11 |

327 | If ( boldsymbol{f}={(boldsymbol{4}, boldsymbol{5}),(boldsymbol{5}, boldsymbol{6}),(boldsymbol{6},-boldsymbol{4})} ) and ( boldsymbol{g}= ) ( {(boldsymbol{4},-boldsymbol{4}),(boldsymbol{6}, boldsymbol{5}),(boldsymbol{8}, boldsymbol{5})} . ) Then ( |boldsymbol{f}-boldsymbol{g}|=? ) | 11 |

328 | set of irrational numbers is ( {sqrt{mathbf{8}}, boldsymbol{pi}} ) A . True B. False | 11 |

329 | ( A-(A-B) ) is equivalent to which expression A. ( B ) в. ( A cup B ) c. ( A cap B ) D. ( B-A ) | 11 |

330 | The set ( S:{1,2,3, ldots ., 12} ) is to be partitioned into three sets ( A, B, C ) of equal size. Thus, ( boldsymbol{A} cup boldsymbol{B} cup boldsymbol{C}=boldsymbol{S}, boldsymbol{A} cap ) ( boldsymbol{B}=boldsymbol{B} cap boldsymbol{C}=boldsymbol{A} cap boldsymbol{C}=boldsymbol{phi} . ) The number of ways to partition ( S ) is A ( cdot frac{12 !}{3 !(4 !)^{3}} ) в. ( frac{12 !}{3 !(3 !)^{4}} ) c. ( frac{12 !}{(4 ! !)^{3}} ) D. ( frac{12 !}{(3 !)^{4}} ) | 11 |

331 | For any two sets ( A ) and ( B, A=B ) is equivalent to This question has multiple correct options ( mathbf{A} cdot A-B=B-A ) ( mathbf{B} cdot A cup B=A cap B ) ( mathbf{c} . A cup C=B cup C ) and ( A cap C=B cap C ) for any set ( C ) ( mathbf{D} cdot A cap B=phi ) | 11 |

332 | If ( boldsymbol{A}=(boldsymbol{6}, boldsymbol{7}, boldsymbol{8}, boldsymbol{9}), boldsymbol{B}=(boldsymbol{4}, boldsymbol{6}, boldsymbol{8}, boldsymbol{1 0}) ) and ( boldsymbol{C}={boldsymbol{x}: boldsymbol{x} boldsymbol{epsilon} boldsymbol{N}: boldsymbol{2}<boldsymbol{x} leq 7} ; ) find : ( boldsymbol{A}-(boldsymbol{B} cup boldsymbol{C}) ) | 11 |

333 | Classify the following set as ‘singleton’ or ’empty’: ( B={y mid y ) is an odd prime number ( <4} ) A. singleton B. Empty c. Data insufficient D. None of these | 11 |

334 | {1,2,3}( nsubseteq{1,3,5} ) as ( m notin{1,3,5} ) Then ( m ) is: | 11 |

335 | Find the intersection of ( A ) and ( B ) by representing using by Venn diagram: ( boldsymbol{A}={boldsymbol{a}, boldsymbol{b}, boldsymbol{c}}, boldsymbol{B}={1,2, boldsymbol{9}} ) ( A cdot phi ) в. ( a, b, c, 1,2,9 ) c. ( a, c, 1,9 ) D. None of these | 11 |

336 | The elements of ( (boldsymbol{A}-boldsymbol{B}) ) are: | 11 |

337 | The numbers shown in the Venn diagram represent the number of elements in each subset. Find ( [(boldsymbol{F} cup ) ( boldsymbol{G}) cap boldsymbol{H}^{prime} ) ( A cdot 3 ) B. 13 ( c cdot 15 ) D. 18 | 11 |

338 | State whether the following statement is true or false. Give reason to support your answer. For any two sets ( A ) and ( B ) either ( A subseteq B ) | 11 |

339 | In the given figure, how many people study only 2 subjects? Mathematics A . 11 ( B .23 ) ( c cdot 12 ) D. 40 | 11 |

340 | A marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used only Brand A soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap? A . 15 B. 20 c. 30 D. 40 E . 45 | 11 |

341 | Prove by using venn diagram ( boldsymbol{A}-(boldsymbol{B} cup boldsymbol{C})=(boldsymbol{A}-boldsymbol{B}) cap(boldsymbol{A}-boldsymbol{C}) ) | 11 |

342 | State, whether the following pairs of sets are equal or not: If they are equal then write 1 , else write ( mathbf{0} ) ( A=2,4,6,8 ) and ( B={2 n: n epsilon N ) and ( boldsymbol{n}<mathbf{5}} ) | 11 |

343 | If ( boldsymbol{A}-boldsymbol{B}=boldsymbol{phi} ) and ( boldsymbol{B}-boldsymbol{A}=boldsymbol{phi} ) then ( mathbf{A} ) and B are A. Overlapping B. Equivalent c. Dissiont D. Equal | 11 |

344 | Every subset of an infinite set is infinite.? | 11 |

345 | The relationship illustrated by the given Venn diagram is : ( mathbf{A} cdot(A cup B) cap C ) ( mathbf{B} cdot(A cap B) cap C ) ( mathbf{c} cdot(A cap C) cup B ) ( mathbf{D} cdot(A cup B)^{prime} cap C ) | 11 |

346 | Find the total number of subsets of each of the following set: ( boldsymbol{C}={boldsymbol{x} mid boldsymbol{x} in boldsymbol{W}, boldsymbol{x} leq 2} ) | 11 |

347 | Set of concentric circle in a plane | 11 |

348 | ( boldsymbol{A}-[boldsymbol{B} cup boldsymbol{C} cup boldsymbol{D}]=(boldsymbol{A}-boldsymbol{B}) cap ldots ldots cap ) A ( . A-C ) and ( A-D ) B. ( C-A ) and ( A-D ) c. ( C-A ) and ( D-A ) D. ( A-C ) and ( D-A ) | 11 |

349 | An investigator interviewed 100 students to determine their preferences for the three drinks : milk (M), coffee (C) and tea (1). He reported the following: 10 students had all the three drinks M, C and T: 20 had M and C: 30 had C and T, 25 had Mand T; 12 had M only: 5 had C only, and 8 had T only. Using a Venn diagram find how many did not take any of the three drinks. (1978) | 11 |

350 | Suppose A1, A2, …….. A30 are thirty sets each with five elements and B, B2, ……. B. are n sets each with thre 30 n . elements. Let U A; = U B; = S. Assume that each i= j=1 element of S belongs to exactly ten of the Ai’s and to exactly | 11 |

351 | If ( zeta ) is the set of boys in your school and ( B ) is the set of boys who play badminton Draw a Venn-diagram showing that some of boys do not play badminton. If ( boldsymbol{n}(boldsymbol{zeta})=mathbf{4 0} ) and ( boldsymbol{n}left(boldsymbol{B}^{prime}right)=mathbf{1 7} ; ) find how many play badminton. | 11 |

352 | The question is based on the Venn Diagram. The circle stands for rural Triangle stands for educated, square stands for hard-working and Rectangle stands for intelligent persons. The number given represents a serial number of the area Which area represents ” Intelligent hard-working and educated but not | 11 |

353 | Which of the following sets is infinite? A. ( {x: x text { is neither prime, nor composite }}, x in N ) B. The set of all rivers in India C. Set of concentric circles D. ( A={x: x text { is a letter of the English alphabet }} ) | 11 |

354 | If ( boldsymbol{X}={1,2,3, dots, 10} ) and ( A= ) ( {1,2,3,4,5} . ) Then, the number of subsets ( B ) of ( X ) such that ( A-B={4} ) is ( A cdot 2^{5} ) B ( cdot 2^{4} ) ( mathbf{c} cdot 2^{5}-1 ) D. E ( .2^{4}-1 ) | 11 |

355 | State true or false. Given universal set= ( = ) ( left{-mathbf{6},-mathbf{5} frac{mathbf{3}}{mathbf{4}},-sqrt{mathbf{4}},-frac{mathbf{3}}{mathbf{5}},-frac{mathbf{3}}{mathbf{8}}, mathbf{0}, frac{mathbf{4}}{mathbf{5}}, mathbf{1}, mathbf{1} frac{mathbf{2}}{mathbf{3}}right. ) From the given set, find set of non- negative integers is {0,1} A. True B. False | 11 |

356 | Find ( A triangle B ) and by definition: ( boldsymbol{A}={mathbf{1}, mathbf{2}, mathbf{3}, mathbf{4}, mathbf{5}} ) and ( boldsymbol{B}={mathbf{1}, mathbf{3}, mathbf{5}, mathbf{7}} ) | 11 |

357 | Let ( A, B ) and ( C ) be sets such that ( phi= ) ( boldsymbol{A} cap boldsymbol{B} subseteq boldsymbol{C} . ) Then which of the following statements is not true? ( mathbf{A} cdot ) If ( (A-C) subseteq B, ) then ( A subseteq B ) в. ( (C cup A) cap(C cup B)=C ) c. If ( (A-B) subseteq C ), then ( A subseteq C ) D. ( B cap C neq phi ) | 11 |

358 | Define subset of a set. | 11 |

359 | Suppose ( U= ) ( {3,4,5,6,7,8,9,10,11,12,13}, A= ) ( {3,4,5,6,9}, B={3,7,9,5} ) and ( C= ) ( {6,8,10,12,7} . ) Write down the following set and draw Venn diagram for: ( boldsymbol{A}^{prime} ) | 11 |

360 | An investigator interviewed 100 students to determine their preferences for the three drinks: milk ( ( M ) ), coffee ( (C) ) and tea ( (T) . ) He reported the following: 10 students had all the three drinks ( M, C, T ; 20 ) had ( M ) and ( C ) only; ( mathbf{3 0} ) had ( boldsymbol{C} ) and ( boldsymbol{T} ; mathbf{1 2} ) had ( boldsymbol{M} ) only ( ; mathbf{5} ) had ( C ) only; 8 had ( T ) only. Then how many did not take any of three drinks is A . 20 B. 30 ( c .36 ) D. 42 | 11 |

361 | If ( boldsymbol{A}={boldsymbol{m}, boldsymbol{a}, boldsymbol{t}, boldsymbol{h}, boldsymbol{e}, boldsymbol{m}, boldsymbol{a}, boldsymbol{t}, boldsymbol{i}, boldsymbol{c}, boldsymbol{s}}, boldsymbol{B}= ) ( {a, m, t, h, e, i, c, s}, ) then: A ( . A=B ) в. ( A neq B ) c. ( A subset B ) D. ( B subset A ) | 11 |

362 | Let ( boldsymbol{A}={mathbf{3}, mathbf{6}, mathbf{1 2}, mathbf{1 5}, mathbf{1 8}, mathbf{2 1}}, boldsymbol{B}= ) ( {mathbf{4}, mathbf{8}, mathbf{1 2}, mathbf{1 6}, mathbf{2 0}}, boldsymbol{C}= ) ( {mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}, mathbf{1 2}, mathbf{1 4}, mathbf{1 6}} ) and ( boldsymbol{D}= ) ( {mathbf{5}, mathbf{1 0}, mathbf{1 5}, mathbf{2 0}} . ) Find ( boldsymbol{A}-boldsymbol{C} ) | 11 |

363 | The set of all animals on the earth is a A. Finite set B. singleton set c. Null set D. Infinite set | 11 |

364 | 000 0 0 ( infty ) 00 | 11 |

365 | The set ( {x: x neq x} ) may be equal to ( A cdot{0} ) B. {1} ( c cdot{3} ) ( D cdot{phi} ) | 11 |

366 | If ( boldsymbol{A}-boldsymbol{B}=emptyset, ) then relation between ( mathbf{A} ) and B is : ( mathbf{A} cdot A neq B ) в. ( B subset A ) ( c . A subset B ) D. ( A=B ) | 11 |

367 | Draw Venn diagrams to illustrate ( boldsymbol{A} backslash boldsymbol{B} ) | 11 |

368 | Let ( boldsymbol{A}={mathbf{3}, mathbf{6}, mathbf{1 2}, mathbf{1 5}, mathbf{1 8}, mathbf{2 1}}, boldsymbol{B}= ) ( {mathbf{4}, mathbf{8}, mathbf{1 2}, mathbf{1 6}, mathbf{2 0}}, boldsymbol{C}= ) ( {mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}, mathbf{1 2}, mathbf{1 4}, mathbf{1 6}} ) and ( boldsymbol{D}= ) ( {mathbf{5}, mathbf{1 0}, mathbf{1 5}, mathbf{2 0}} . ) Find ( boldsymbol{A}-boldsymbol{D} ) | 11 |

369 | The following is an example of empty set: ( {x: x text { is a natural number, } xmathbf{1 2}} ) A. True B. False | 11 |

370 | The shaded region in the Venn diagram represents | 11 |

371 | The Venn diagram shows sets ( P, Q ) and ( R ) with regions labelled, I, II, III and IV. State the region which represents set ( left[boldsymbol{P} cap(boldsymbol{Q} cup boldsymbol{R})^{prime}right] ) 4 B. ( c ) ( D cdot|v| ) | 11 |

372 | In a group, if ( 60 % ) of people drink tea and ( 70 % ) drink coffee. What is the maximum possible percentage of people drinking either tea or coffee but not both? ( mathbf{A} cdot 100 % ) B. ( 70 % ) ( c .30 % ) D. ( 10 % ) | 11 |

373 | In the Venn diagram, the universal set, ( boldsymbol{xi}=boldsymbol{P} cup boldsymbol{Q} cup boldsymbol{R} ) Which of the four regions labelled ( A, B, C ) and D represents the sets ( boldsymbol{P} cap boldsymbol{Q} cap boldsymbol{R} ) ? ( A ) B ( c . c ) ( D ) | 11 |

374 | Let ( boldsymbol{A}={mathbf{3}, mathbf{6}, mathbf{1 2}, mathbf{1 5}, mathbf{1 8}, mathbf{2 1}}, boldsymbol{B}= ) ( {mathbf{4}, mathbf{8}, mathbf{1 2}, mathbf{1 6}, mathbf{2 0}}, boldsymbol{C}= ) ( {mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}, mathbf{1 2}, mathbf{1 4}, mathbf{1 6}} ) and ( boldsymbol{D}= ) ( {mathbf{5}, mathbf{1 0}, mathbf{1 5}, mathbf{2 0}} . ) Find ( boldsymbol{D}-boldsymbol{A} ) | 11 |

375 | If ( boldsymbol{B}=left{boldsymbol{y} mid boldsymbol{y}^{2}=boldsymbol{3} boldsymbol{6}right} ) then the ( operatorname{set} boldsymbol{B} ) is a set. A. Empty B. singleton c. Infinite D. None of the above | 11 |

376 | The shaded region in the adjoining diagram represents A ( . A-B ) B. ( B-A ) ( mathbf{c} cdot A Delta B ) D. ( A ) | 11 |

377 | In a class of 50 students 35 opted for Mathematics and 37 opted for Biology How may have opted for only Mathematics? (Assume that each student has to opt for at least one of the subjects) A . 15 B. 17 c. 13 D. 19 | 11 |

378 | In the Venn diagram, ( boldsymbol{xi}=boldsymbol{F} cup boldsymbol{G} cup boldsymbol{H} ) The shaded region in the diagram represents set ( A cdot(F cap H)^{prime} cup G ) в. ( (F cup H) cap G ) c. ( G cup(F cap H) ) D. ( G cap(F cup H) ) | 11 |

379 | Which of the following is equivalent set (i) ( boldsymbol{A}={mathbf{2}, mathbf{3}, mathbf{5}, mathbf{7}} ) (ii) ( B={a, e, i, o, u} ) (iii) ( boldsymbol{C}={-mathbf{1},-mathbf{9},-mathbf{8},-mathbf{7}} ) A. (i) and (ii) B. (i) and (iii) c. (ii) and (iii) D. None of these | 11 |

380 | If ( boldsymbol{A} cap boldsymbol{B} subseteq boldsymbol{C} ) and ( boldsymbol{A} cap boldsymbol{B} neq boldsymbol{phi} ). Then which of the following is incorrect ( mathbf{A} cdot(A cup B) cap C neq phi ) в. ( B cap C=phi ) c. ( A cap C neq phi ) D. If ( (A-C) subseteq C ) then ( A subseteq C ) | 11 |

381 | reflexive, symmetric and transitive. This question has multiple correct options ( A cdot R_{3}={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1)} ) ( mathbf{B} cdot R_{3}= ) ( {(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(1,3),(3,1),(4, ) ( mathbf{c} cdot R_{3}={(1,1),(2,2),(3,3),(4,4)} ) D. none of these | 11 |

382 | If ( M={b, h, i} ; N={b, c, d, e} ) and ( boldsymbol{S}={boldsymbol{e}, boldsymbol{f}, boldsymbol{g}}, ) determine ( boldsymbol{M} cap boldsymbol{N} cap boldsymbol{S} ) and represent it in a Venn diagram. | 11 |

383 | Draw venn diagram ( boldsymbol{A} cup(boldsymbol{B} cap boldsymbol{C}) ) | 11 |

384 | From the given diagram find the number of elements in ( left(A^{prime} cup B^{prime}right) ) | 11 |

385 | Find total number of subsets of ( {p: p ) is a letter in the word ‘poor’? | 11 |

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